.\" DO NOT MODIFY THIS FILE!  It was generated by help2man 1.49.3.
.TH PRIMES.PL "1" "March 2024" "primes.pl version 1.3 using Math::Prime::Util 0.73 and MPU::GMP 0.52" "User Commands"
.SH NAME
primes.pl \- Display all primes
.SH SYNOPSIS
.B primes
[\fI\,options\/\fR]  [\fI\,START\/\fR]  \fI\,END\/\fR
.SH 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).
.PP
General options:
.TP
\fB\-\-help\fR
displays this help message
.PP
Filter options, which will cause the list of primes to be further filtered
to only those primes additionally meeting these conditions:
.TP
\fB\-\-twin\fR
Twin             p+2 is prime
.TP
\fB\-\-triplet\fR
Triplet          p+6 and (p+2 or p+4) are prime
.TP
\fB\-\-quadruplet\fR Quadruplet
p+2, p+6, and p+8 are prime
.TP
\fB\-\-cousin\fR
Cousin           p+4 is prime
.TP
\fB\-\-sexy\fR
Sexy             p+6 is prime
.TP
\fB\-\-safe\fR
Safe             (p\-1)/2 is also prime
.TP
\fB\-\-sophie\fR
Sophie Germain   2p+1 is also prime
.TP
\fB\-\-lucas\fR
Lucas            L_p is prime
.TP
\fB\-\-fibonacci\fR
Fibonacci        F_p is prime
.TP
\fB\-\-mersenne\fR
Mersenne         M_p = 2^p\-1 is prime
.TP
\fB\-\-lucky\fR
Lucky            p is a lucky number
.TP
\fB\-\-palindr\fR
Palindromic      p is equal to p with its base\-10 digits reversed
.TP
\fB\-\-pillai\fR
Pillai           n! % p = p\-1 and p % n != 1 for some n
.TP
\fB\-\-good\fR
Good             p_n^2 > p_{n\-i}*p_{n+i} for all i in (1..n\-1)
.TP
\fB\-\-cuban1\fR
Cuban (y+1)      p = (x^3 \- y^3)/(x\-y), x=y+1
.TP
\fB\-\-cuban2\fR
Cuban (y+2)      p = (x^3 \- y^3)/(x\-y), x=y+2
.TP
\fB\-\-pnp1\fR
Primorial+1      p#+1 is prime
.TP
\fB\-\-pnm1\fR
Primorial\-1      p#\-1 is prime
.TP
\fB\-\-euclid\fR
Euclid           pn#+1 is prime
.TP
\fB\-\-circular\fR
Circular         all digit rotations of p are prime
.TP
\fB\-\-panaitopol\fR Panaitopol
p = (x^4\-y^4)/(x^3+y^3) for some x,y
.TP
\fB\-\-provable\fR
Ensure all primes are provably prime
.PP
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 \fB\-\-\fR the least value of the set.
.SH AUTHOR
Written by Dana Jacobsen.