- **Puzzles**
(*https://www.mersenneforum.org/forumdisplay.php?f=18*)

- - **3, 7, 31, 127**
(*https://www.mersenneforum.org/showthread.php?t=24255*)

3, 7, 31, 127What do these have in common?
This list may very well be complete. |

[QUOTE=petrw1;512504]What do these have in common?
This list may very well be complete.[/QUOTE]Things that make me go MM |

Only known instance where four consecutive primes, p, for which 2[SUP]p[/SUP]-1 is prime?
That is, where p[SUB]n[/SUB] is the nth prime and M(x) represents 2[SUP]x[/SUP]-1, then: M(p[SUB]n[/SUB]) M(p[SUB]n+1[/SUB]) M(p[SUB]n+2[/SUB]) M(p[SUB]n+3[/SUB]) are all prime. |

[QUOTE=petrw1;512504]What do these have in common?
This list may very well be complete.[/QUOTE] Exponents of double Mersenne primes ( = Mersenne primes p such that 2^p - 1 is also a Mersenne prime). Mersenne numbers that are also lucky numbers. |

I thought this was too easyThe only 4 numbers so far that are:
- exponents of MPs - an MP 7 for example: [TEX]2^3-1 = 7[/TEX] and [TEX]2^7-1 = 31[/TEX] The next candidate may be a few years away: (TEX wasn't behaving here) 2[SUP]31[/SUP] = 2147483647 2[SUP]2147483647[/SUP] -1 = xxx Is xxx a prime? |

[QUOTE=petrw1;512568]The only 4 numbers so far that are:
- exponents of MPs - an MP[/QUOTE]I think lukerichards also gave a plausible answer. |

[QUOTE=retina;512570]I think lukerichards also gave a plausible answer.[/QUOTE]
For sure, my oversight....and Serge too. |

[QUOTE=petrw1;512568]
The next candidate may be a few years away: (TEX wasn't behaving here) 2[SUP]31[/SUP] = 2147483647 [/QUOTE] I find TEX doesn't like superscripts of more than 1 digit unless you put them in curly braces. e.g.: [CODE] [TEXX]2^{31}-1[/TEXX] [/CODE] (I've slipped an extra x into the tag to stop it rendering TEX within the code block.) Which gives: [TEX]2^{31}-1[/TEX] |

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