primes (1)

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.

General options:

--help

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

Twin p+2 is prime

--triplet

Triplet p+6 and (p+2 or p+4) are prime

--quadruplet Quadruplet

p+2, p+6, and p+8 are prime

--cousin

Cousin p+4 is prime

--sexy

Sexy p+6 is prime

--safe

Safe (p-1)/2 is also prime

--sophie

Sophie Germain 2p+1 is also prime

--lucas

Lucas L_p is prime

--fibonacci

Fibonacci F_p is prime

--mersenne

Mersenne M_p = 2^p-1 is prime

--lucky

Lucky p is a lucky number

--palindr

Palindromic p is equal to p with its base-10 digits reversed

--pillai

Pillai n! % p = p-1 and p % n != 1 for some n

--good

Good p_n^2 > p_{n-i}*p_{n+i} for all i in (1..n-1)

--cuban1

Cuban (y+1) p = (x^3 - y^3)/(x-y), x=y+1

--cuban2

Cuban (y+2) p = (x^3 - y^3)/(x-y), x=y+2

--pnp1

Primorial+1 p#+1 is prime

--pnm1

Primorial-1 p#-1 is prime

--euclid

Euclid pn#+1 is prime

--circular

Circular all digit rotations of p are prime

--panaitopol Panaitopol

p = (x^4-y^4)/(x^3+y^3) for some x,y

--provable

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.