Highly experimental personal projects. https://trizenx.blogspot.com/
trizen
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modified: oeis-research/Giorgos Kalogeropoulos/Least positive integer not already in the sequence with the property that the concatenation a(0)a(1)...a(n) forms an integer with n distinct prime factors/prog.sf
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README.md
experimental-projects
Highly experimental personal projects.
Summary
- Aliquot-sequences
- Can-you-find
- Cgi-projects
- Cicada-3301
- Factordb
- Gnfs
- Highly-composite-numbers
- Oeis-drafts
- Oeis-research
- Ahmad J. Masad
- Albert Böschow
- Alex Costea
- Alex Ratushnyak
- Alexander Adamchuk
- Alexander R. Povolotsky
- Indices of squares in A068869
- No "n" exist, such that ( n! + prime(n) ) = m^k, where k>1%20)%20=%20m^k,%20where%20k>1)
- prog.pl%20)%20=%20m^k,%20where%20k>1/prog.pl)
- Altug Alkan
- A(n) is the smallest k such that psi(k) = factorial(n)
- A(n) is the smallest k such that usigma(k) = primorial(n)
- Carmichael numbers n such that n-1 is a perfect power
- Composite integers n such that the sum of the Pell numbers is divisible by n
- Integers n such that n-th prime divides the n-th golden rectangle number
- Integers n such that the n-th prime divides the n-th Pell number
- Least k such that k is the product of n distinct primes and sigma(k) is an n-th power
- Least k such that k^n + 1 is the product of n distinct primes
- Least k such that phi(k) is an n-th power when k is the product of n distinct primes
- Least k such that sigma(k) is a Fibonacci number when k is the product of n distinct primes
- Least prime p such that p^n + 1 is the product of n distinct primes
- Smallest k such that psi(k) and phi(k) have same distinct prime factors when k is the product of n distinct primes
- Amarnath Murthy
- A(1) = 1, for n>1 a(n) = largest prime divisor of A062273(n)
- A(1) = 2, a(n+1) = a(n)-th squarefree number
- A(n) = the largest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n
- A(n) = the largest prime divisor of the number C(n) formed from the reverse concatenation of 1,2,3,... up to n
- Least k such that k*prime(k) > 10^n
- Smallest k such that n, k and n+k have the same prime signature
- Smallest number sandwiched between two numbers having exactly n prime divisors
- Smallest prime which is 1 more than a product of n distinct primes: a(n) is a prime and a(n) - 1 is a squarefree number with n prime factors
- Sum of the remainders when n^2 is divided by squares < n
- Amiram Eldar
- A(n) is the least number k such that gpf(k)^n | k and gpf(k+1)^n | (k+1)
- A(n) is the least number k such that the n-th odd squarefree divides lcm(1..k) over denom(harmonic(k))
- A(n) is the least start of exactly n consecutive numbers k that are sqrt(k)-smooth (A048098), or -1 in no such run exists
- A(n) is the minimum number of distinct numbers with exactly n prime factors (counted with multiplicity) whose sum of reciprocals exceeds 1
- Abundant Carmichael numbers
- Bi-unitary divisors sum constant
- Chernick-Carmichael number n prime factors
- Colltaz with sqrt(3) or 3
- Composite numbers (pseudoprimes) n, that are not Carmichael numbers, such that A000670(n) == 1 (mod n)
- Consecutive numbers whose sum of divisors has the same set of distinct prime divisors
- Least k > 1 such that sigma(k) * phi(k) is an n-th perfect power
- Least number k such that A046660(k) = A046660(k+1) = n
- Least number k such that A048105(k) = A048105(k+1) = 2*n, and 0 if it does not exist
- Least number k such that there are exactly n cubefull numbers between k^3 and (k+1)^3
- Least start of a run of exactly n successive powerful numbers that are pairwise coprime
- Least super-Poulet number with n distinct prime factors
- Let k be the n-th perfect number, a(n) is the least number m such that k*d*m + 1 is prime for all of the proper divisors d of k so their product is a Carmichael number
- Lexicographically earliest sequence of numbers whose partial products are all Fermat pseudoprimes to base 2
- Lexicographically earliest sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2
- Lexicographically earliest strictly increasing sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2
- Number of abundant numbers < 10^n
- Number of primitive abundant numbers (A071395) < 10^n
- Numbers k such that A168512(2^k) is a prime number
- Numbers k such that F(k), F(k+1) and F(k+2) have the same binary weight (A000120), where F(k) is the k-th Fibonacci number (A000045)
- Numbers k such that gpf(k)^2 | k and gpf(k+1)^3 | (k+1)
- Numbers k such that gpf(k)^2 | k and gpf(k+1)^4 | (k+1)
- Numbers k such that gpf(k)^3 | k and gpf(k+1)^2 | (k+1)
- Numbers k such that gpf(k)^4 | k and gpf(k+1)^2 | (k+1)
- Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor
- Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer
- Numbers m such that sigma(m) is a Lucas number
- Numbers n such that n = pi(n) + uphi(n)
- Numbers n such that sigma(n) and sigma(n)-n are both triangular numbers
- Numbers that are both infinitary and noninfinitary harmonic numbers
- Numbers that are both unitary and nonunitary harmonic numbers
- Numbers that are not powers of primes whose harmonic mean of their proper unitary divisors is an integer
- Odd numbers that are not safe primes such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1
- Poulet numbers with a record number of divisors that are also Poulet numbers
- Poulet numbers with records of abundancy
- Quadratic Mersenne primes for alpha = 2 + sqrt(2)
- Semi-unitary perfect numbers
- The number of terms of A354558 that are <= 10^n
- Unitary harmonic numbers (A006086) that are not unitary arithmetic numbers (A103826)
- Antti Karttunen
- Arkadiusz Wesolowski
- Arsen Vardanyan
- Artsiom Palkounikau
- Artur Jasinski
- Benoit Cloitre
- Bernard Schott
- 5^n ends in n
- A(n) is the largest prime < 10^n obtained with the longest sum of consecutive primes
- A(n) is the smallest integer that has exactly n Lucas divisors
- Brazilian primes constant
- Largest prime whose decimal expansion consists of the concatenation of the largest n-digit primes
- Smallest exclusionary square (A029783) with exactly n distinct prime factors.
- Smallest Niven (or Harshad) number (A005349) with exactly n distinct prime factors
- Smallest number m such that tau(k) * k = m has n solutions
- Smallest Zuckerman number (A007602) with exactly n distinct prime factors
- Bodo Zinser
- Brad Clardy
- Chai Wah Wu
- Charles R Greathouse IV
- Charles T. Le
- Charlie Neder
- Cino Hilliard
- Clark Kimberling
- Claude H. R. Dequatre
- Claudio Meller
- Colin Barker
- Ctibor O. Zizka
- César Aguilera
- Daniel Hoya
- Daniel Lignon
- Daniel Suteu
- A(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1)
- Agrawal's conjecture pseudoprimes
- Alternating sum of the Mertens function
- Carmichael numbers k such that k+1 is divisible by gpf(k)+1
- Carmichael numbers k where records occur for gcd(k-1, lambda(k))
- Carmichael numbers n where records occur for gpf(n) divided by lpf(n)
- Carmichael numbers n where records occur for lpf(n) divided by gpf(n)
- Carmichael-Lucas-Carmichael almost numbers
- Chernick-Carmichael numbers
- Chernick-Carmichael numbers with 4 or more prime factors
- Chernick-Carmichael numbers with k factors
- Cubic recurence sequence
- Difference of 0's and 1's in middle of binary digits
- Digit scrambling sequences
- Dirichlet convolution of 2^omega(n)*mu(n)^2 with the positive integers
- Emirps
- Factor sequences
- Fermat pseudoprimes of the form p*((p-1)*n + 1)
- Generalized class of primes
- Incrementally largest numbers n that are the product of primes p such that p+1 divides n
- Irregular triangle read by rows of integers k such that n AND k != k, for k = 1..n
- Irregular triangle read by rows of integers k such that n AND k = k, for k = 1..n
- Large smooth semiprime
- Least non-palindromic number k such that k and its digital reversal both are the product of n distinct primes
- Least number k such that A002277(k) has exactly n distinct prime factors
- Limit for pi ÷ 4
- Liouville sum
- Moebius transform of dedekind
- Number k such that tau(k) equals the number of solutions to sigma(x) = k
- Number of distinct prime factors of sigma(sigma n(n))
- Number of primes factors of the n-th n-powerful number
- Numbers k such that (prime(k) - composite(k)) == 0 (mod k)
- Numbers k such that phi(k) = factorial of sum of digits of k
- Numbers n such that omega(sigma(n,n)) = bigomega(sigma(n,n))
- Numbers n such that sigma(n)+1 divides n*(tau(n)+1)
- Odd squarefree composite integers n such that prev prime(p)-1 | n-1 and next prime(p)-1 | n-1 for every p|n
- OEIS Conjecture
- Other
- Other programs
- Palindromic pseudoprimes in base n
- Partial sums of 2^(bigomega(n) - omega(n))
- Partial sums of dirichlet convolution of the prime characterstic function with itself
- Partial sums of inverse moebius transform of 2^bigomega(n)
- Partial sums of moebius inversion of (-1)^omega
- Partial sums of sums of prime powers
- Records of sigma0 for p^2-1
- Reversal of prime p is composite in all bases 2..n
- Riemann prime counting function
- Romanian numbers
- Sierpiński triangle
- Smallest base-n strong Fermat pseudoprime with n distinct prime factors
- Smallest Carmichael number (A002997) with n prime factors that is also a strong pseudoprime to base 2 (A001262)
- Smallest Carmichael number such that gpf(p-1) = prime(n)
- Smallest Fermat base-2 pseudoprime such that gpf(p-1) = prime(n)
- Smallest number k > 0 such that bigomega(k^n + 1) = n
- Smallest number k > 1 such that bigomega(k^n - 1) = n
- Smallest overpseudoprime to base 2 (A141232) with n distinct prime factors
- Smallest palindrome with n prime factors
- Smallest squarefree palindrome with exactly n distinct palindromic prime factors
- Square array A(n, k) read by antidiagonals downwards: smallest base-n strong Fermat pseudoprime with k distinct prime factors for k, n >= 2
- Surprising chaotic finite sequence
- TODO
- Add new terms to A076960
- Add terms to A305058
- Factorization of n^n-(n-1)^(n-1)
- Factorization of n^n + (n+1)^(n+1)
- Is power plus minus
- Iterative functions - Sidef
- More terms for continued fractions periods
- Number of 0's minus number of 1's binary
- Prime p such that p-1 has a record number of divisors d such that 2^d == 1 mod p
- Primes between composite numbers
- Darío Clavijo
- David James Sycamore
- Carmichael divisible by sum of factors
- Numbers k such that if j is the sum of the first k primes, then the sum of the first j primes is prime
- Numbers k such that prime(k)^k - primorial(k - 1) is prime
- Prime indexed primes
- Primes p such that if k is the sum of the first p primes then the sum of the first k primes is prime
- Smallest prime number whose a056240-type is n
- Derek Orr
- Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists
- Least prime p such that p^n and p^n+1 have the same number of prime factors (counted with multiplicity) or 0 if no such number exists
- Smallest number m such that m and reverse(m) each have n distinct prime factors
- Donovan Johnson
- Eder Vanzei
- Eduard Roure Perdices
- Elliott Line
- Erich Friedman
- Falcon Shapiro
- Farideh Firoozbakht
- Felix Fröhlich
- 3-powerful numbers = sum of two coprime 3-powerful numbers
- Both truncatable primes
- Composite k such that binomial(2k, k) = 2 that are not squares or cubes of primes
- Felix truncatable primes
- Smallest base-n Fermat pseudoprime with n distinct prime factors
- Square array A(n, k) read by antidiagonals downwards: smallest base-n Fermat pseudoprime with k distinct prime factors for k, n >= 2
- Fernando Solanet Mayou
- G. L. Honaker, Jr.
- Gionata Neri
- Giorgos Kalogeropoulos
- Giovanni Resta
- Gonzalo Martínez
- Greg Dresden
- Gus Wiseman
- Hans Havermann
- Howard Berman
- Hugo Pfoertner
- Numbers k such that (3^k + 3*k) over 3 is prime
- Numbers k such that (4^k + 4*k) over 4 is prime
- Numbers k such that lucasu(3, -8, k) is prime
- Numbers k such that Product {j=1..k} prime(j) + Product {j=k+1..2*k} prime(j) is prime
- Numbers n such that 2^n + n + 2 is prime
- Numbers n such that n^(n + 1) + n - 1 is prime
- Numbers n such that n^4 + 4^n is a semiprime
- Ilya Gutkovskiy
- A(n) is the index of the smallest square pyramidal number divisible by exactly n square pyramidal numbers
- Consecutive integers with equal bigomega(n) - omega(n)
- Consecutive integers with equal sigma0(n) - omega(n)
- Index of the smallest Fibonacci n-step number with exactly n distinct prime factors
- Index of the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity)
- Index of the smallest n-gonal number divisible by exactly n n-gonal numbers
- Index of the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers
- Index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity)
- Index of the smallest tetrahedral number with exactly n distinct prime factors
- Index of the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists
- Index of the smallest tetranacci number (A000078) with exactly n distinct prime factors
- Index of the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity)
- Index of the smallest tribonacci number (A000073) with exactly n distinct prime factors
- Index of the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity)
- Least number k such that the average number of prime divisors of {1..k} counted with multiplicity is >= n
- Maximal coefficient of (1 + x^a(1)) * (1 + x^a(1) + x^a(2)) * ... * (1 + x^a(1) + x^a(2) + ... + x^a(n-1))
- N-th prime recursive sum
- Number of subsets of {1..n} whose harmonic mean is an integer
- Numbers k such that the average number of odd divisors of {1..k} is an integer
- Perfect powers that are equal to the sum of the first k perfect powers > 1 for some k
- Smallest centered n-gonal number divisible by exactly n centered n-gonal numbers
- Smallest centered n-gonal number with exactly n distinct prime factors
- Smallest centered n-gonal number with exactly n prime factors (counted with multiplicity)
- Smallest centered square number divisible by exactly n centered square numbers
- Smallest centered square number with exactly n distinct prime factors
- Smallest centered square number with exactly n prime factors (counted with multiplicity)
- Smallest centered triangular number with exactly n distinct prime factors
- Smallest centered triangular number with exactly n prime factors (counted with multiplicity)
- Smallest n-gonal number divisible by exactly n n-gonal numbers
- Smallest n-gonal number with exactly n distinct prime factors
- Smallest n-gonal number with exactly n prime factors (counted with multiplicity)
- Smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers
- Smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists
- Smallest n-gonal pyramidal number with exactly n distinct prime factors
- Smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity)
- Smallest number k such that n consecutive integers starting at k have the same number of triangular divisors
- Smallest number that is the sum of two distinct n-th powers of primes in two different ways
- Smallest number which can be represented as the product of n distinct integers > 1 in exactly n ways
- Smallest number with exactly n divisors that are n-gonal numbers
- Smallest positive integer which can be represented as the sum of distinct positive Fibonacci n-step numbers (with a single type of 1) in exactly n ways, or -1 if no such integer exists
- Smallest square pyramidal number with exactly n distinct prime factors
- Squarefree harmonic sum exceeds n
- Irina Gerasimova
- Ivan N. Ianakiev
- J. Lowell
- J. M. Bergot
- A(n) is the first number k with A340967(k) = n
- A(n) is the first prime p such that, with q the next prime, p + q^2 is 10^n times a prime
- A(n) is the first prime p such that, with q the next prime, p^2+q is 10^n times a prime
- A(n) is the first prime that is the start of a sequence of exactly n primes under the map p -> p + sopfr(p-1) + sopfr(p+1)
- A(n) is the first prime that starts a sequence of exactly n consecutive primes prime(k+1), ..., prime(k+n) where prime(k+i)+2^i is prime for i = 1...n but not for i = n+1
- A(n) is the first prime that starts a string of exactly n consecutive primes that are in A347702
- A(n) is the least k such that bigomega(k)=n and bigomega(k+1)=n+1
- A(n) is the least prime p such that bigomega(p+n) = bigomega(p-n) = n
- A(n) is the least prime p such that p^2+4 is a prime times 5^n
- A(n) is the least prime p such that there exists a prime q with p^2 + n = (n+1)*q^2, or 0 if there is no such p
- A(n) is the least prime p that is the first of three consecutive primes p, q, r such that p^i + q^i - r^i is prime for i from 1 to n but not n+1
- A(n) is the least prime prime(k) such that prime(k+n-1)^2 - prime(k)^2 + prime(i) for i=k..k+n-1 are consecutive primes
- First emirp p that starts a sequence of n emirps x(1),...,x(n) with x(1) = p and x(k+1) = 2*x(k) - reverse(x(k)), but 2*x(n) - reverse(x(n)) is not an emirp
- Numbers k such that A124440(k) is a square
- Numbers k such that prime(k)^prime(k+1) == prime(k+3) (mod prime(k+2))
- Numbers k such that the k-th triangular number mod sopfr(k), and the k-th triangular number mod sigma(k), are the same prime
- Primes p such that (2^p+p^2) over 3 is prime
- Primes p such that the sum of squares of primes < p is divisible by p
- Primes p such that, with q the next prime after p, q > p+2 and q^p == q (mod p+q) and p^q == p (mod p+q)
- Semiprimes p*q with p <= q such that Sum {primes r <= p} (q mod r) = q
- Smallest k having n prime factors such that k + sum of the prime factors of k also has n prime factors
- Smallest k such that n = bigomega(k) = bigomega(k-1) + bigomega(k+1)
- Smallest prime p such that p-1 and p+1 both have n prime factors (with multiplicity)
- J.W.L. (Jan) Eerland
- Jacques Tramu
- James S. DeArmon
- Jaroslav Krizek
- Jason Earls
- A(1) = 1, a(n) = largest prime divisor of A057137
- Largest prime factor of 9^(2n)+1 (A063270)
- Largest prime factor of A019518, concatenation of first n primes
- Largest prime factor of the integer formed by truncating the decimal expansion of Pi to n places
- Number of brilliant numbers < 10^n
- Number of factors of distinct prime factors of sum of p n primorials
- Numbers that set a new record for number of Fibonacci divisors
- Prime pi equals sum of primes lpf and gpf
- Jean-Marc Rebert
- Jeff Burch
- Jeppe Stig Nielsen
- Jianing Song
- Jinyuan Wang
- Least totient number k > 1 such that n*k is a nontotient number, or 0 if no such number exists
- Numbers k such that 4^k - 3^k + 2^k is prime
- Run of n primes when 3*x - 2 is iterated
- Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime
- Jon E. Schoenfield
- Jonathan Sondow
- Jonathan Vos Post
- Joseph Biberstine
- José María Grau Ribas
- Numbers n such that phi(n) divides n+1, where phi is Euler's totient function (A000010))
- erdos generation method.pl/erdos_generation_method.pl)
- from smooth multiple.sf/from_smooth_multiple.sf)
- inverse phi.pl/inverse_phi.pl)
- smooth generate.pl/smooth_generate.pl)
- Numbers n such that phi(n) divides n+1, where phi is Euler's totient function (A000010))
- Jud McCranie
- Julien Peter Benney
- Juri-Stepan Gerasimov
- A(n) is the least k>1 such that omega(k) is equal to (omega(n*k + 1) - 1) over n
- Integers k such that the k-th prime divides the k-th Lucas number
- Largest prime factor of n^n - n^(n-1) - n^(n-2) - ... - n^2 - n - 1
- Numbers k such that k^4*2^k - 1 is a prime
- Numbers k such that omega(2^k-1) = omega(2*k-1)
- Numbers n such that n^(n + 1)*(n + 1)^n + 1 is prime
- Numbers q such that (4*q^2-1)*2^q + 1 is prime
- Primes p such that 2^p - p^2 is prime
- Smallest positive number k such that k^2 - 1 and k^2 + 1 each have n distinct prime divisors
- Smallest prime p such that A005117(k+1) - A005117(k-1) = n, where p = A005117(k) for some k
- Smallest prime p such that bigomega(p^n - 2) = bigomega(p^n + 2) = n
- Sum of remainders of the n-th composite mod k, for k=1..n
- Kevin Batista
- Kevin P. Thompson
- Kevin Ryde
- Klaus Brockhaus
- Labos Elemer
- A(n) = tau( sigma n(n) ), where tau is the number of divisors of n
- Index of smallest prime p such that there is a gap of 2^n between p and next prime
- Largest prime divisor of n-th primorial + (n+1)-st prime
- Least k > 0 such that sigma(factorial(k)) >= n*factorial(k)
- Least k such that nextprime(k^n) - prevprime(k^n) = 4
- Number of different terms in the period of sqrt cfrac of repunits
- Number of nonsquarefree numbers not exceeding n
- Number of powerful numbers between 2^(n-1)+1 and 2^n
- Numbers k such that Cyclotomic(k,k) is prime
- Smallest x such that prime(x) mod composite(x) = n
- Lekraj Beedassy
- Leroy Quet
- Lorenzo Sauras Altuzarra
- Luis H. Gallardo
- M. F. Hasler
- Highly composite numbers - twin primes
- Indices of Tribonacci primes
- Largest prime factor of A001008(n), numerator of n-th harmonic number
- Least odd primitive abundant number with n prime factors, counted with multiplicity
- Numbers k such that Omega(k) = Omega(2^k-1), where Omega(k) is the number of prime factors of k counted with multiplicity (A001222)
- Numbers of the form N = a+b+c such that N^3 = concat(a,b,c)
- Sum of sigma(n) mod k for k = 1..n-1
- M. Farrokhi D. G.
- Maheswara Rao Valluri
- Manuel Valdivia
- Marco Ripà
- Marius A. Burtea
- Matthew Campbell
- Max Alekseyev
- Max Z. Scialabba
- Metin Sariyar
- Numbers k such that (prime(k) + composite(k)) == 0 (mod k)
- Numbers k such that sigma(k) = factorial of sum of digits of k
- Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k
- Numbers m such that Sum {k=1..m} omega(k) = sigma(m)
- Numbers n such that sum of first k composites k^k is prime
- Start of the first run of n consecutive primes using only prime digits
- Sum of first n prime powers of 2 + prime(n+1) is prime
- Twin prime and prime-indices emirps
- Michael S. Branicky
- Michel Lagneau
- Least k such that prime(k) + prime(k+1) contains n prime divisors
- Numbers k such that sigma 2(Fibonacci(k)^2 + 1) == 0 (mod Fibonacci(k))
- Semiprimes p-q is divisilbe by 2^n
- Smallest number k such that k and k+1 are both of the form p*q^n where p and q are distinct primes
- Smallest number k such that k^n + 1 contains n distinct prime divisors
- Smallest number such that k^2 + 1 has n distinct prime factors
- Smallest number such that k^n - 1 contains n distinct prime divisors
- Smallest prime factor of p^p - 1 that is congruent to 1 modulo p where p = prime(n)
- Michel Marcus
- A(n) is the least integer m such that M(m) is divisible by prime(n)^2 or -1 if no such m exists
- Exponents d of powers of 2, q, such that each of q-1 and q+1 are either a power of prime or a semiprime
- Integers k such that A110299(k) is prime
- Integers m such that m and m+1 are terms of A111035
- Least integer k such that the inverse of sum of inv(phi(k+j)) for j=1..n is an integer
- Least Lucas number with n Lucas divisors
- Least number k such that the concatenation of k composites from composite(n) is prime
- Number of Lucas divisors of the n-th Lucas number
- Prime p for which the continued fraction expansion of sqrt(p) has exactly n consecutive 1's starting at position 2
- Primes p such that the greatest common divisor of 2^p+1 and 3^p+1 is composite
- Primes where every 0-splitting is prime
- Smallest m such that gcd of the x's that satisfy sigma(x) = m is n%20=%20m%20is%20n)
- comb.sf%20=%20m%20is%20n/comb.sf)
- search.pl%20=%20m%20is%20n/search.pl)
- smooth generate.pl%20=%20m%20is%20n/smooth_generate.pl)
- sort upperbounds.sf%20=%20m%20is%20n/sort_upperbounds.sf)
- Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers
- Smallest number k such that sigma(sigma(k)) >= n*k
- Sum of first k divisors equal j+1 for non-squares of primes
- Mohammed Bouayoun
- Muniru A Asiru
- N. J. A. Sloane
- A(1)=3, b(n) = Product {k=1..n} a(k), a(n+1) is the largest prime factor of (b(n)-1)
- A(n) = largest prime factor of the number with decimal expansion 20305070...0p n where p n = n-th prime
- A(n) is the largest prime factor of 2^p - p^2 where p is the n-th prime
- Carmichael numbers of special form
- Euclid-Mullin sequence: a(1) = 2, a(n+1) is largest prime factor of Product {k=1..n} a(k) + 1
- Largest prime factor of (p^p-1) over (p-1) where p = prime(n)
- Largest prime factor of concatenation of primes with zeros
- Least Carmichael number with n prime factors, or 0 if no such number exists
- Numbers n such that sigma(sigma(n)) = n*k
- Records in A073053
- Smallest divisor of the Motzkin number not already in the sequence
- Solution to x = 3*tanh(x)
- Zeros of an alternating sum of Euler totients
- Zeros of an alternating sum of primes sequence
- Naohiro Nomoto
- Nicolas Bělohoubek
- Oliver Townsend
- Olivier Gérard
- Omar E. Pol
- Ovidiu Bagdasar
- Paolo Galliani
- Paolo P. Lava
- A(n) is the maximum prime factor of the concatenation of a(n-2) and a(n-1), with a(1)=1 and a(2)=2
- A(n) is the maximum prime factor of the concatenation of all the previous terms, with a(1)=1, a(2)=2
- Least number such that the concatenation of all the previous terms with it is squarefree and has n prime factors
- Numbers k such that k divides sigma(k-2) + sigma(k-1) + sigma(k+1) + sigma(k+2)
- Quasi-narcissistic numbers: k-digit numbers n whose sum of k-th powers of their digits is equal to n +- 1
- Smallest composite number with n distinct prime factors with property that the concatenation of its distinct prime factors, in descending order, is a palindrome
- Squarefree difference of semiprimes
- Paolo Xausa
- Patrick De Geest
- A(n)-th prime has exactly n zeros
- Index of smallest repunit having exactly n prime factors (counted with multiplicity)
- Palindromes of form n^2 + (n+1)^2
- Smallest composite number with n distinct prime factors with property that the concatenation of its distinct prime factors is a palindrome
- Smallest fraction using palindromes that approximates Pi
- Smallest palindrome with exactly n palindromic prime factors (counted with multiplicity), and no other prime factors
- Smallest squarefree palindrome with exactly n distinct prime factors
- Paul Vanderveen
- Peter Kagey
- Peter Luschny
- Petros Hadjicostas
- Philip Mizzi
- Pierre CAMI
- Pontus von Brömssen
- Ralf Stephan
- Reinhard Zumkeller
- Richard N. Smith
- Richard Pinch
- Rick L. Shepherd
- Robert FERREOL
- Robert G. Wilson v
- A(n) is obtained by applying the map k -> prime(k) n times, starting at n
- Index of first occurence of n in splitting function
- Index of first occurence of n in splitting function -- upper-bounds
- Least semiprime for which n-1 iterations of "Look & Say" (A045918) all yield semiprimes, but not the n-th iteration%20all%20yield%20semiprimes,%20but%20not%20the%20n-th%20iteration)
- prog.pl%20all%20yield%20semiprimes,%20but%20not%20the%20n-th%20iteration/prog.pl)
- Number of 13-smooth numbers <= 10^n
- Number of positive integers <= 10^n that are divisible by no prime exceeding p
- Numbers k such that 8*factorial(k)-1 is prime
- Smallest prime p such that bigomega(p+nextprime(p)) = n
- The number of n-almost primes less than or equal to 10^n, starting with a(0)=1
- The number of n-almost primes less than or equal to 12^n, starting with a(0)=1
- The number of n-almost primes less than or equal to 8^n, starting with a(0)=1
- The number of n-almost primes less than or equal to 9^n, starting with a(0)=1
- The smallest k such that k! + 1 has exactly n prime factors (with multiplicity)
- Robert Israel
- A(n) is the first prime p such that, if q is the next prime, (p*q+p+q) is 5^n times a prime
- A(n) is the first prime that begins a sequence of exactly n consecutive primes that are emirps
- A(n) is the least k such that k^j+2 is prime for j = 1 to n but not n+1
- A(n) is the least number that has exactly n divisors with sum of digits n
- First number that is the sum of k successive semiprimes for 1 <= k <= n
- First prime p such that p - 2 and p + 2 both have exactly n prime factors, counted with multiplicity
- Indices k such that A002533(k) is prime
- Least k > 1 such that all divisors of (k^n-1) over (k-1) are == 1 (mod n)
- Least k for which A237196(k) = n
- Least n-gonal number that is the product of n distinct primes, or 0 if there are none
- Least number of the form p^2 + q^2 - 2 for primes p and q that is an odd prime times 2^n, or -1 if there is no such number
- Least semiprime that is the first of n consecutive semiprimes s(1) ... s(n) such that s(i) - prime(i) are all equal
- Numbers k such that 10^k + 3 is a semiprime
- Numbers n such that binary(n) == 1 mod n
- Positions of records in A306440
- Primes prime(k) such that prime(k)^2 + prime(k+1)^2 - 1 is the square of a prime
- Squares in A213544
- Robert Price
- Ryan Propper
- Rémy Sigrist
- Scott R. Shannon
- Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition
- Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition, when written in binary
- Composite numbers that divide the reverse of the concatenation of their ascending order prime factors, with repetition
- Smallest positive number that has yet appeared such that the sum of all terms a(1) + ... + a(n) has the same number of prime factors
- The smallest composite number k that shares exactly n distinct prime factors with sopfr(k), the sum of the primes dividing k, with repetition
- The smallest number whose prime factor concatenation, when written in base n, contains all digits 0,1,...,(n-1)
- Seiichi Manyama
- Sergio Pimentel
- Sezai Ata
- Shyam Sunder Gupta
- Carmichael numbers which are also base-2 strong pseudoprimes
- Index of smallest Fibonacci number with n prime factors when counted with multiplicity
- Palindromic pseudoprimes to base 2
- Smallest titanic number with 3 distinct prime factors
- Smallest triangular number with n prime factors (counted without multiplicity)
- Sidney Cadot
- Sofia Lacerda
- Stefano Spezia
- T. D. Noe
- Tejo Vrush
- Thomas Gajdek
- Thomas Ordowski
- 12 June
- 12 May
- 13 June
- 13 May
- 15 May
- 17 May
- 18 May
- 2 July 2019
- 22 July - comments
- 24 May
- 9 June
- A(n) is the smallest b > 0 such that b^(2n) + 1 has all prime divisors p == 1 (mod 2n)
- A(n) is the smallest k with n prime factors such that p^k == p (mod k) for every prime p dividing k
- A(n) is the smallest number k with n prime factors such that p + div(k,p) is prime for every prime p | k
- A(n) is the smallest odd b > 1 such that (b^(2n) + 1) over 2 has all prime divisors p == 1 (mod 2n)
- Conjecture 13 July 2022
- Divisibility of numerators of harmonic numbers
- Factor 2n
- Least k > 1 such that all divisors d of (k^(2n+1)+1) over (k+1) satisfy d == 1 (mod 2n+1)
- Non-residue pseudoprimes
- Primes sum of squares
- Smallest k such that 2^(2^n+1)-1 + 2^k is prime, or -1 if no such k exists
- Super-poulet conjecture
- Thomasz a and b sequences
- Tomasz base = 5 primes
- Tomasz mod 1 divisors
- Tomasz new sequences
- Tomasz p+1 semiprimes
- Tomasz rad p+1 pseudoprimes
- Tomasz rad p-1 pseudoprimes
- Tomasz squarefree conjecture
- Tomazs znorder primes
- Tim Johannes Ohrtmann
- Least Carmichael number that is divisible by the n-th cyclic number A003277(n), or 0 if no such number exists
- Least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number
- Least Lucas-Carmichael number with n prime factors
- Number of eleven-prime Carmichael numbers less than 10^n
- Number of Lucas-Carmichael numbers less than 10^n
- Numbers n such that (9^n + 7^n) ÷ 16 is prime
- Tomohiro Yamada
- Tony Davie
- Torbjorn Alm
- Vincenzo Librandi
- Vladimir Letsko
- Vladimir Shevelev
- Wesley Ivan Hurt
- Ya-Ping Lu
- Yasutoshi Kohmoto
- Yusuf Gurtas
- Zak Seidov
- 6^n is the sum of two consecutive primes
- A(n) = sigma 2(a(n-1)), with a(1) = 2
- A(n) is the least k > a(n-1) such that k - a(i) for i = 0 .. n-1 all have exactly n prime factors, counted with multiplicity; a(0) = 0
- A(n) is the least odd number k such that Omega(k) = n, Omega(k+2) = n+1, and Omega(k+4) = n+2
- A(n) is the smallest even number k such that k-1 and k+1 are both n-almost primes
- A(n) is the smallest number m such that m, m+1, m+2 and m+3 each have exactly n prime factors (counted with multiplicity)
- Concatenation of numbers from n to a(n) is prime
- First n-almost prime after 3^n
- First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1
- First prime p such that, if q are r are the next two primes, p + r, p + q, q + r and p + q + r all have n prime divisors, counted with multiplicity
- Least k that starts a sequence of exactly n numbers on which i + Omega(i) is constant
- Least number k such that 3^k-2 and 3^k+2 are the product of n prime factors counted with multiplicity
- Least odd number k such that Omega(k) = n, Omega(k+2) = n+1, and Omega(k+4) = n+2
- Least prime p such that the concatenation p|n has exactly n prime factors with multiplicity
- Numbers k that are the sum and product of 5 consecutive primes
- Prev prime and next prime same nr of factors
- Primes p congruent to 1..10 mod 11
- Primes p congruent to 1..8 mod 13
- Smallest prime p cogruent to 1..prime(n)-1 mod prime(n)
- Zhao Hui Du
- Pseudoprimes
- 620-programs
- $620 generation.sf
- 620 research.pl
- 620 research PSW.pl
- 620 fermat generator.pl
- 620 from big prime list.pl
- 620 from big prime list 2.pl
- 620 from big prime list 3.pl
- 620 lucas-fibonacci pseudoprimes.sf
- 620 research with D.pl
- 620 strong fermat generator.pl
- 620 strong generator.pl
- carmichael euler phi.pl
- carmichael pseudoprimes.sf
- create primes.pl
- create primes 2.pl
- pseudoprimes comb.pl
- Generators
- almost strong fermat psp from multiple.pl
- carmichael-lucas-carmichael from multiple recursive mpz.pl
- carmichael-lucas-carmichael from prime factors unbounded mpz.pl
- carmichael-lucas-carmichael number generation mpz.pl
- carmichael almost lucas-carmichael from prime factors.pl
- carmichael from combinations.sf
- carmichael from combinations of primes recursive mpz.pl
- carmichael from multiple recursive mpz.pl
- carmichael generate.pl
- carmichael in range from prime factors.pl
- carmichael large from prime factors.pl
- carmichael numbers in range.pl
- carmichael numbers in range with prefix.pl
- carmichael numbers in range with prefix mpz.pl
- carmichael numbers p==3 mod 80 in range.pl
- carmichael with n prime factors from prime factors.pl
- erdos carmichael from lambdas.pl
- erdos carmichael generate from prefix.pl
- erdos carmichael with prefix from lambda.pl
- erdos generate carmichael shuffle.pl
- erdos generate carmichael with prefix.pl
- erdos generate carmichal.pl
- erdos generate fibonacci from lambdas.pl
- erdos lucas-carmichael from lambdas.pl
- erdos lucas-carmichael generation.pl
- erdos lucas-carmichael with prefix.pl
- erdos special carmichael with multiple.pl
- fermat from generated primes.pl
- fermat from lambdas.pl
- fermat from lucas sequences.sf
- fermat pseudoprimes from prime factors with p+1 smooth.pl
- fermat pseudoprimes generation.jl
- fermat pseudoprimes in range.pl
- fermat pseudoprimes in range with prefix.pl
- fermat pseudoprimes in range with prefix mpz.pl
- fermat pseudoprimes p==3 mod 80 in range.pl
- fermat pseudoprimes with small znorder.sf
- fermat strong pseudoprimes from prime factors.pl
- fermat superpseudoprimes from prime factors.pl
- generate abundant carmichael numbers.pl
- generate carmichael-hebyshev pseudoprimes.pl
- generate carmichael cyclic multiple.pl
- generate carmichael of second order.pl
- generate carmichael of second order 2.pl
- generate carmichael of second order 3.pl
- generate carmichael overpseudoprimes.pl
- generate carmichael overpseudoprimes.sf
- generate carmichael superpseudoprimes.pl
- generate chebyshev pseudoprimes.pl
- generate chernick-like carmichael numbers.sf
- generate fermat overpseudoprimes.pl
- generate fermat overpseudoprimes 2.pl
- generate fermat p==3 (mod 80).pl
- generate fermat pseudoprimes.pl
- generate fermat psp from multiples.pl
- generate fermat psp from multiples v2.pl
- generate fermat psp to multiple bases from prime factors.pl
- generate fermat psp with 620 primes.pl
- generate fermat superpseudoprimes.pl
- generate frobenius pseudoprimes.pl
- generate large carmichael with k factors.sf
- generate lucas-carmichael multiple.pl
- generate lucas pseudoprimes.pl
- generate psp from primorials.sf
- generate psp from primorials 2.sf
- generate psp from root.sf
- generate PSW counter-example.sf
- generate psw counter-example from prime factors.pl
- generate williams number from prime factors.pl
- generate williams numbers.pl
- generate williams numbers.sf
- imprimitive carmichael.sf
- imprimitive carmichael better.sf
- imprimitive carmichael coin change.sf
- inverse znorder generation.sf
- larger carmichael from carmichael.sf
- larger carmichael from carmichael simple.sf
- larger fermat from fermat.sf
- larger fermat from fermat simple.sf
- larger fermat from fermat with variations.sf
- lucas-carmichael.pl
- lucas-carmichael from combinations.sf
- lucas-carmichael in range from prime factors.pl
- lucas-carmichael numbers in range.pl
- lucas-carmichael unbounded from prime factors from lambdas.pl
- lucas carmichael divisible by n.pl
- lucas psp from lambdas.pl
- non-residue generate.pl
- odd abundant cyclic numbers.sf
- odd almost abundant cyclic numbers.sf
- odd almost abundant lucas-cyclic numbers.sf
- pomerance generate smooth primes.pl
- psp from psp.pl
- psp from smooth primes.pl
- psp from smooth primes extra.pl
- recursively generate carmichael.sf
- recursively generate fermat from znorder.sf
- recursively generate fermat from znorder with variations.sf
- recursivley generate carmichael.pl
- recursivley generate lucas psp.pl
- search lucas-carmichael from multiple.pl
- special form carmichael.sf
- squarefree fermat pseudoprimes in range.pl
- squarefree strong fermat psp with n prime factors.pl
- strong carmichael with n prime factors from prime factors.pl
- strong fermat psp with n prime factors from prime factors.pl
- strong fermat psp with n prime factors from prime factors 2.pl
- super poulet pseudoprimes.pl
- super poulet pseudoprimes from prime file.pl
- super poulet pseudoprimes with generated primes.pl
- Primes
- Programs
- 2^(k-1) == (2*k + 1) (mod k^2).pl
- 2^(k-1) == (2*k + 1) (mod k^2) db.pl
- 2^(k-1) == (2*k + 1) (mod k^2) primes db.pl
- 2n+1 is carmichael.pl
- abundancy index records psp2.pl
- abundant carmichael.pl
- abundant carmichael cached.pl
- abundant fermat pseudoprimes.pl
- abundant fermat pseudoprimes cached.pl
- abundant lucas-carmichael.pl
- abundant lucas-carmichael cached.pl
- almost-extra-strong-lucas not extra-strong-lucas.pl
- almost abundant carmichael.pl
- almost carmichael pseudoprime.pl
- almost carmichael pseudoprime cached.pl
- almost carmichael pseudoprime db.pl
- antti lehmer problem.pl
- antti lehmer problem smooth numbers.pl
- benoit primes 1 cached.pl
- benoit primes 2 cached.pl
- bfw pseudoprime db.pl
- binary period pseudoprimes.pl
- binary search in file.pl
- bpsw pseudoprime 1.pl
- bpsw pseudoprime 2.pl
- bpsw pseudoprime 3.pl
- bpsw pseudoprime 4.pl
- bpsw pseudoprime db.pl
- Cache
- carmichael-bernoulli kn numbers cached.pl
- carmichael-bernoulli numbers cached.pl
- carmichael-lucas-carmichael from factors cached.pl
- carmichael divisible by 255 cached.pl
- carmichael from divisors.pl
- carmichael from super psp cached.pl
- carmichael gcd is carmichael cached.pl
- carmichael gpf(p-1) = prime(n).pl
- carmichael in range cached.pl
- carmichael is fibonacci cached.pl
- carmichael lambda.pl
- carmichael lambda+1 is prime cached.pl
- carmichael lambdas cached.pl
- carmichael lcm factor is carmichael.pl
- carmichael lcm is carmichael cached.pl
- carmichael m-1 is power.pl
- carmichael m-1 is power cached.pl
- carmichael m-1 is square.pl
- carmichael multiples of cyclic numbers upper-bounds.pl
- carmichael multiples of cyclic numbers upper-bounds cached.pl
- carmichael n-2 and n+2 are prime.pl
- carmichael of order 2.pl
- carmichael of order 2 cached.pl
- carmichael of order 2 from factors cached.pl
- carmichael of order 4 cached.pl
- carmichael overpseudoprimes cached.pl
- carmichael p==3 mod 80.pl
- carmichael p==3 mod 80 cached.pl
- carmichael phi-lambda conjecture cached.pl
- carmichael rad(p-1)==rad(n-1) cached.pl
- carmichael rad(p-1)==rad(n-1) db.pl
- carmichael strong psp with n factors cached.pl
- carmichael superpseudoprimes.pl
- carmichael superpseudoprimes cached.pl
- carmichael where gpf(n)+1|n+1.pl
- carmichael where gpf(n)+1|n+1 cached.pl
- carmichael where p+1|n+1.pl
- carmichael where phi(k) does not divide (k-1)^n cached.pl
- carmichael with 3 factors p+1|n+1.pl
- carmichael with 3 factors p+1|n+1 cached.pl
- carmichael with consecutive factors cached.pl
- carmichael with gcd phi lambda cached.pl
- carmichael with large lehmer index cached.pl
- carmichael with only odd digits cached.pl
- central polygonal carmichael.pl
- chebyshev pseudoprimes.pl
- consecutive fermat.pl
- consecutive fermat below 2^64.pl
- eldar carmichael numbers cached.pl
- emirp carmichael cached.pl
- euler jacobi psp to first n bases db.pl
- euler jacobi psp to first n bases txt.pl
- euler trinomial strong psp.pl
- extra-strong lucas not lucas.pl
- factorize pseudoprime.pl
- factorize pseudoprimes.pl
- factors of 2^n-1 overpseudoprimes.pl
- factors of 2^n-1 psp.pl
- factors of 2^n-1 strong psp.pl
- factors of mersenne.pl
- fermat3 m-1 is square.pl
- fermat 2^n == 2 (mod n*(n-1)).pl
- fermat 2n+1 is pseudoprime.pl
- fermat base n with n factors.pl
- fermat from divisors.pl
- fermat from fermat cached.pl
- fermat gpf(p-1) = prime(n).pl
- fermat m-1 is cube.pl
- fermat p==3 mod 80.pl
- fermat p==3 mod 80 bellow 2^64.pl
- fermat p==3 mod 80 cached.pl
- fermat p==3 mod 80 db.pl
- fermat psp with n factors db.pl
- fermat with large lehmer index cached.pl
- fermat with n factors where p-1 does not divide k-1.pl
- fermat with n factors where p-1 does not divide k-1 cached.pl
- fermat with n factors where p-1 does not divide k-1 db.pl
- fib n and n+1 divides sum of fib.pl
- five consecutive odd pseudoprimes.pl
- frobenius pseudoprime.pl
- gauss-euler counterexample.pl
- gauss-euler counterexample db.pl
- generate carmichael with p==q mod 12 comb db.pl
- generate carmichael with p==q mod 12 db.pl
- generate pseudoprimes from factors.pl
- generate pseudoprimes from factors cached.pl
- generate psp from prime factors db.pl
- generate psp from psp db.pl
- giuga conjecture.pl
- giuga conjecture cached.pl
- imprimitive carmichael with n factors.pl
- imprimitive carmichael with n factors cached.pl
- is bpsw pseudoprime.pl
- is euler-fibonacci pseudoprime.pl
- is frobenius khashin pseudoprime.pl
- is frobenius pseudoprime.pl
- is frobenius underwood pseudoprime.pl
- is mpz pseudoprime.pl
- is perrin pseudoprime.pl
- is quadratic frobenius pseudoprime.pl
- janfeitsma contains check.pl
- lambda carmichael numbers cached.pl
- largest ndigit carmichael.pl
- largest ndigit carmichael cached.pl
- largest ndigit pseudoprime.pl
- largest ndigit pseudoprime cached.pl
- lehmer totient conjecture.pl
- lehmer totient conjecture cached.pl
- lehmer totient weak numbers cached.pl
- lehmer totient weak numbers native.pl
- lucas(n)==2 mod n.pl
- lucas-carmichael-fermat pseudoprime cached.pl
- lucas-carmichael conjecture.pl
- lucas-carmichael conjecture cached.pl
- lucas-carmichael gcd is term cached.pl
- lucas-carmichael lambda+1 is prime cached.pl
- lucas-carmichael lambdas cached.pl
- lucas-carmichael lcm is term cached.pl
- lucas-carmichael multiples of lucas-cyclic numbers.pl
- lucas-carmichael multiples of lucas-cyclic numbers cached.pl
- lucas-carmichael plus 1 divides sigma(n).pl
- lucas-carmichael where gpf(n)-1|n-1 cached.pl
- lucas-carmichael with 3 factors p-1|n-1.pl
- lucas-carmichael with 3 factors p-1|n-1 cached.pl
- lucas-carmichael with large lehmer index cached.pl
- lucas-carmichael with n factors.pl
- lucas-carmichael with n factors cached.pl
- lucas-fermat conjecture cached.pl
- lucas-fermat pseudoprime.pl
- lucas restricted domain primality test.sf
- lucas V pseudoprimes.pl
- n+1 divides sigma(n) db.pl
- new psp2.pl
- nine nine nine pseudoprimes.pl
- non-pandigital carmichael cached.pl
- non-residue fermat records.pl
- non-residue fermat records below 2^64.pl
- non-residue pseudoprimes.pl
- non-residue pseudoprimes below 2^64.pl
- nonsquarefree pseudoprimes.pl
- odd part of carmichael-1 is carmichael.pl
- Other
- batch gcd factorization.sf
- BPSW primality test.pl
- BPSW primality test anynum.pl
- BPSW primality test mpz.pl
- check factordb.sf
- fib-tzn primality test.pl
- fib-tzn primality test.sf
- fib-tzn strong primality test.pl
- find bfw psp.sf
- math-anynum.pl
- pseudoprime factorization.sf
- PSW primality test.pl
- PSW primality test ntheory.pl
- test.pl
- test2.pl
- test3.pl
- test fermat fib.pl
- test fib-tzn.pl
- test fib prime.pl
- overpseudoprimes with n factors cached.pl
- palindromic fibonacci.pl
- palindromic lucas.pl
- palindromic pseudoprimes.pl
- palindromic pseudoprimes in base n.pl
- phi(k) divides k-3.pl
- phi(n) divides n+1 db.pl
- pomerance fib test.pl
- pomerance smooth primes cached.pl
- pomerance smooth primes from factors.pl
- primary carmichael with n prime factors cached.pl
- prime gaps db.pl
- pseudoprime surrounded by primes.pl
- pseudoprimes of the form 6p+1.pl
- pseudoprimes with only odd digits.pl
- reversible lucas.pl
- reversible pseudoprimes.pl
- safe pseudoprimes.pl
- similar lehmer totient weak numbers native.pl
- smallest carmichael-kronecker with n factors cached.pl
- smallest carmichael with n factors.pl
- smallest carmichael with n factors cached.pl
- smallest fermat with n factors.pl
- smallest fermat with n factors cached.pl
- smallest fibonacci psp with n factors.pl
- smallest k such that p^k==p (mod k).pl
- smallest ndigit carmichael.pl
- smallest ndigit carmichael cached.pl
- smallest ndigit pseudoprime.pl
- smallest ndigit pseudoprime cached.pl
- smallest strong pseudoprime to the first n bases cached.pl
- smallest strong pseudoprime to the first n prime bases cached.pl
- smallest superpseudoprime to the first n bases cached.pl
- smooth primes.pl
- smooth primes 2.pl
- solovay strassen pseudoprimes.pl
- steuerwald-ordowsk theorem.pl
- strong miller rabin pseudoprimes.pl
- strong miller rabin pseudoprimes cached.pl
- strong psp n-2 and n+2 are prime.pl
- strong psp with n prime factors.pl
- super-poulet with n factors.pl
- super-poulet with n factors cached.pl
- super primitive primes.pl
- superpseudoprimes.pl
- superpseudoprimes cached.pl
- tomasz A309284 db.pl
- tomasz A309285 db.pl
- tomasz pseudoprimes cached.pl
- twin lucas.pl
- twin pseudoprimes.pl
- very strong lucas.pl
- wall-sun-sun primes cached.pl
- weak lucas.pl
- wieferich primes.pl
- wieferich primes cached.pl
- wilson primes cached.pl
- Util
- verify new carmichael.pl
- 620-programs
- Sloane-gap