Display all primes


primes [,options/] [,START/] ,END/


Displays all primes between the positive integers START and END, inclusive. The START and END values must be integers or simple expressions. This allows inputs like "10**500+100" or "2**64-1000" or "2 * nth_prime(560)". Additionally, if END starts with '+' then it is assumed to add to START. If only one number is given, primes up to that number are shown (START = 0).

General options:

displays this help message

Filter options, which will cause the list of primes to be further filtered to only those primes additionally meeting these conditions:

Twin p+2 is prime
Triplet p+6 and (p+2 or p+4) are prime
--quadruplet Quadruplet
p+2, p+6, and p+8 are prime
Cousin p+4 is prime
Sexy p+6 is prime
Safe (p-1)/2 is also prime
Sophie Germain 2p+1 is also prime
Lucas L_p is prime
Fibonacci F_p is prime
Mersenne M_p = 2^p-1 is prime
Lucky p is a lucky number
Palindromic p is equal to p with its base-10 digits reversed
Pillai n! % p = p-1 and p % n != 1 for some n
Good p_n^2 > p_{n-i}*p_{n+i} for all i in (1..n-1)
Cuban (y+1) p = (x^3 - y^3)/(x-y), x=y+1
Cuban (y+2) p = (x^3 - y^3)/(x-y), x=y+2
Primorial+1 p#+1 is prime
Primorial-1 p#-1 is prime
Euclid pn#+1 is prime
Circular all digit rotations of p are prime
--panaitopol Panaitopol
p = (x^4-y^4)/(x^3+y^3) for some x,y
Ensure all primes are provably prime

Note that options can be combined, e.g. display only safe twin primes. In all cases involving multiples (twin, triplet, etc.), the value returned is p -- the least value of the set.


Written by Dana Jacobsen.