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Old 2019-04-03, 05:43   #1
petrw1
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"Wayne"
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Default 3, 7, 31, 127

What do these have in common?

This list may very well be complete.
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Old 2019-04-03, 05:54   #2
retina
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Quote:
Originally Posted by petrw1 View Post
What do these have in common?

This list may very well be complete.
Things that make me go MM
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Old 2019-04-03, 07:40   #3
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"Luke Richards"
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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.
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Old 2019-04-03, 12:14   #4
Batalov
 
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Quote:
Originally Posted by petrw1 View Post
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.
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Old 2019-04-03, 17:52   #5
petrw1
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Default 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?
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Old 2019-04-03, 17:54   #6
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Quote:
Originally Posted by petrw1 View Post
The only 4 numbers so far that are:
- exponents of MPs
- an MP
I think lukerichards also gave a plausible answer.
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Old 2019-04-03, 18:22   #7
petrw1
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Quote:
Originally Posted by retina View Post
I think lukerichards also gave a plausible answer.
For sure, my oversight....and Serge too.
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Old 2019-04-04, 07:17   #8
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Quote:
Originally Posted by petrw1 View Post
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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