20190210, 21:30  #1 
May 2018
2^{2}×61 Posts 
Large gaps between Wagstaff prime exponents
The last few Wagstaff prime exponents have large gaps between them. The next Wagstaff prime exponent after 374321 is 986191, which is more than twice the previous number. Then, it jumps to 4031399. That is more than quadruple the last exponent. Is the next number 13347311? Then, there would be 3 times in a row with a number more than twice the last number. That is very weird.

20190210, 21:54  #2  
Sep 2003
A19_{16} Posts 
Quote:
Also in 2013, Ryan Propper discovered the Wagstaff primes 13347311 and 13372531. He searched at least parts of the 10, 11, 12 and 13 million ranges, but it wasn't clear from his posts whether he covered those ranges exhaustively or only in part. His post mentioned that he calculated ordinary PRP residues. I am currently doublechecking this range, finding and publishing PRP residues (see this miniwebsite). I am using 128 Skylake cores for this and the latest mprime version 29.5. So far I've reached 8.7 million and will probably get to 10 million sometime next month. I'm hoping to find something, but at this point I suspect that there are no new Wagstaff primes to be found below 14 million. 

20190303, 19:37  #3 
May 2018
2^{2}·61 Posts 
374321, 986191, 4031399, 13347311, 13372531
There are 3 big gaps and a very small gap. It is amazing. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Gaps between maximal prime gaps  Bobby Jacobs  Prime Gap Searches  52  20200822 15:20 
Large Gaps >500,000  mart_r  Prime Gap Searches  119  20170821 12:48 
New Wagstaff PRP exponents  ryanp  Wagstaff PRP Search  26  20131018 01:33 
30th Wagstaff prime  T.Rex  Math  0  20070904 07:10 
very large exponents  pacionet  Data  4  20051104 20:10 