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 2019-04-03, 05:43 #1 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 23×211 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

2×23×137 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 28810 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

59×163 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 113658 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

2·23·137 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

23·211 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

25·32 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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