20190403, 05:43  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
12F6_{16} Posts 
3, 7, 31, 127
What do these have in common?
This list may very well be complete. 
20190403, 05:54  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×23×137 Posts 

20190403, 07:40  #3 
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}×3^{2} 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. 
20190403, 12:14  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2591_{16} Posts 

20190403, 17:52  #5 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2·3·809 Posts 
I thought this was too easy
The only 4 numbers so far that are:
 exponents of MPs  an MP 7 for example: and The next candidate may be a few years away: (TEX wasn't behaving here) 2^{31} = 2147483647 2^{2147483647} 1 = xxx Is xxx a prime? 
20190403, 17:54  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×23×137 Posts 

20190403, 18:22  #7 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2×3×809 Posts 

20190404, 07:17  #8  
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}×3^{2} Posts 
Quote:
Code:
[TEXX]2^{31}1[/TEXX] Which gives: 
