# primes - Online in the Cloud

This is the command primes that can be run in the OnWorks free hosting provider using one of our multiple free online workstations such as Ubuntu Online, Fedora Online, Windows online emulator or MAC OS online emulator

### PROGRAM:

#### 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

--twin Twin p+2 is prime

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

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.

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