Mersenne Prime

[Gerson W. Barbosa]

MP:


%%HP: T(3)A(R)F(.);

\<< DUP LN DUP \pi * 4 SWAP / 1 + UNROT / * IP 2 { 2 } ROT 2 SWAP

  START SWAP NEXTPRIME DUP UNROT DUP 2 SWAP ^ 1 - 4 PICK3 2 - 1 SWAP

    START SQ 2 - OVER MOD

    NEXT NIP NOT { + } { DROP } IFTE

  NEXT NIP

\>>

110 MP  -->  { 2 3 5 7 13 17 19 31 61 89 107 }               ( 50 s, HP 50g  )

607 MP  -->  { 2 3 5 7 13 17 19 31 61 89 107 127 521 607 }   (250 s, Emulator)

References:


1) Mersenne Prime

2) Lucas–Lehmer primality test


P.S.: Version using local variables, for clarity

%%HP: T(3)A(R)F(.);

\<< DUP LN DUP \pi * 4 SWAP / 1 + UNROT / * IP 2 { 2 } ROT 2 SWAP

  START SWAP NEXTPRIME DUP 2 SWAP ^ 1 - 4 \-> p m s

    \<< 1 p 2 -

      START s SQ 2 - m MOD 's' STO

      NEXT p DUP UNROT s NOT { + } { DROP } IFTE

    \>>

  NEXT NIP

\>>

Edited: 6 Oct 2013, 10:43 p.m.