3, 7, 31, 127

petrw1 · 2019-04-03, 05:43

What do these have in common?

This list may very well be complete.

retina · 2019-04-03, 05:54

Quote:

Originally Posted by petrw1

What do these have in common?

This list may very well be complete.

Things that make me go MM

lukerichards · 2019-04-03, 07:40

Only known instance where four consecutive primes, p, for which 2^p-1 is prime?

That is, where p_n is the nth prime and M(x) represents 2^x-1, then:

M(p_n)
M(p_n+1)
M(p_n+2)
M(p_n+3)

are all prime.

Batalov · 2019-04-03, 12:14

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.

petrw1 · 2019-04-03, 17:52

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
2^2147483647 -1 = xxx

Is xxx a prime?

retina · 2019-04-03, 17:54

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.

petrw1 · 2019-04-03, 18:22

Quote:

Originally Posted by retina

I think lukerichards also gave a plausible answer.

For sure, my oversight....and Serge too.

lukerichards · 2019-04-04, 07:17

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:

$2^{31}-1$

2019-04-03, 05:43	#1
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 43×107 Posts	3, 7, 31, 127 What do these have in common? This list may very well be complete.

2019-04-03, 17:52	#5
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 1000111111001₂ 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 2^2147483647 -1 = xxx Is xxx a prime?

2019-04-03, 07:40	#3
lukerichards "Luke Richards" Jan 2018 Birmingham, UK 2⁵·3² Posts	Only known instance where four consecutive primes, p, for which 2^p-1 is prime? That is, where p_n is the nth prime and M(x) represents 2^x-1, then: M(p_n) M(p_n+1) M(p_n+2) M(p_n+3) are all prime.