20190403, 05:43  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
5·19·47 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
5,879 Posts 

20190403, 07:40  #3 
"Luke Richards"
Jan 2018
Birmingham, UK
100100000_{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
9158_{10} Posts 

20190403, 17:52  #5 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
5·19·47 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
5,879 Posts 

20190403, 18:22  #7 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
1000101110001_{2} 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: 
