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 2019-04-03, 05:43 #1 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 3·37·47 Posts 3, 7, 31, 127 What do these have in common? This list may very well be complete.
2019-04-03, 05:54   #2
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

199E16 Posts

Quote:
 Originally Posted by petrw1 What do these have in common? This list may very well be complete.
Things that make me go MM

 2019-04-03, 07:40 #3 lukerichards     "Luke Richards" Jan 2018 Birmingham, UK 12016 Posts Only known instance where four consecutive primes, p, for which 2p-1 is prime? That is, where pn is the nth prime and M(x) represents 2x-1, then: M(pn) M(pn+1) M(pn+2) M(pn+3) are all prime.
2019-04-03, 12:14   #4
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,901 Posts

Quote:
 Originally Posted by petrw1 What do these have in common? This list may very well be complete.
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.

 2019-04-03, 17:52 #5 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 3·37·47 Posts I thought this was too easy The only 4 numbers so far that are: - exponents of MPs - an MP 7 for example: $2^3-1 = 7$ and $2^7-1 = 31$ The next candidate may be a few years away: (TEX wasn't behaving here) 231 = 2147483647 22147483647 -1 = xxx Is xxx a prime?
2019-04-03, 17:54   #6
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

11001100111102 Posts

Quote:
 Originally Posted by petrw1 The only 4 numbers so far that are: - exponents of MPs - an MP
I think lukerichards also gave a plausible answer.

2019-04-03, 18:22   #7
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

3×37×47 Posts

Quote:
 Originally Posted by retina I think lukerichards also gave a plausible answer.
For sure, my oversight....and Serge too.

2019-04-04, 07:17   #8
lukerichards

"Luke Richards"
Jan 2018
Birmingham, UK

1001000002 Posts

Quote:
 Originally Posted by petrw1 The next candidate may be a few years away: (TEX wasn't behaving here) 231 = 2147483647
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]
(I've slipped an extra x into the tag to stop it rendering TEX within the code block.)

Which gives:

$2^{31}-1$

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