NAME

       primes.pl - Display all primes

SYNOPSIS

       primes [options]  [START]  END

DESCRIPTION

       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:

       --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.

AUTHOR

       Written by Dana Jacobsen.

primes.pl version 1.3 using Math::Prime::Util ... October 2024                                      PRIMES.PL(1)