20170430, 15:31  #23  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·1,657 Posts 
Quote:
the first (PR)prime value for n>=10^{11} is p(100000135540) and has 352269 decimal digits. 

20170430, 16:59  #24 
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 Posts 

20220703, 01:40  #25 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3×1,657 Posts 
Recently some folks submitted a few more prime partition numbers to UTM Partitions primes.
I ran some stepstone"just test that CMecpp works" candidates to prove and an interesting factoid reared its (fairly trivial) head: a) generally, on average there could be a prime partitions number for each decimal length, and ... b) there is a prime with exactly 20,000 decimal digits in length, but: c) there isn't with 25,000 decimal digits (smallest above is 25,002 decimal digits long) and d) there isn't with 30,000 decimal digits (smallest above is 30,001 decimal digits long)... e) there is a prime with exactly 40,000 decimal digits in length 
20220713, 19:33  #26 
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 Posts 
After almost filling the top20 Partitions primes table with numbers above 13k digits, with our E6 prover code, and starting to eat our own tail, we notice Serge's submissions at 14k digits and so we are now embarking on index 350000000+ i.e. over 20k digits.
Last fiddled with by paulunderwood on 20220713 at 19:45 
20220714, 01:14  #27 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·1,657 Posts 
I decided to run some that will push the 13kers out of relevancy by the top20 limit.
Or else Chuck likely has another few hundred to run ... one after another, day by day. My imagination is too limited to understand the point of proving each consecutive 13,000+ digit prime partition number. Maybe if I do 15 of the same (but 14,000+ digits) I will get enlightened and will understand?! 
20220714, 06:57  #28 
Sep 2002
Database er0rr
2^{2}·3^{2}·7·17 Posts 
You'll be enlightened soon. CM is is a joy with its MPI abilities. Like you say, a prime a day. It is so much fun in comparison to running Primo. Chuck is cutting back to one every 10 days

20220714, 07:11  #29 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·1,657 Posts 
Same random faceless numbers. Just a bit larger.
Wouldn't it be more interesting to find them with a bit of spice, like  p(n) and p(n+1) are prime. E.g. n = 2, 1085, <next term?>  A355728  p(n) is prime and a member of a twin prime pair  A355704, A355705, A355706  p(n^{2}) is prime. Oh. Wait. I've already done this sequence (I did cubes too) 
20220714, 07:32  #30  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
Quote:


20220715, 00:20  #31 
"Oliver"
Sep 2017
Porta Westfalica, DE
481_{16} Posts 

20220715, 05:07  #32 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23326_{8} Posts 
Wrote a sieve and ran some range and found a few large sequence elements (e.g. p(2335166)); will run for some more.
And credit where credit is due: look at the state of p(2335166) in FactorDb, eh? It has been proven by Greg around March, so Greg also is not a foreigner in the land of fun. (Interestingly p(2335166) existed, but p(2335166)+2 didn't exist in FactorDb until I entered it.) A355704, A355705, A355706 
20220715, 08:27  #33  
Apr 2020
857 Posts 
Quote:
Hint: do the partition numbers grow exponentially? Second hint: the probability that p(n) is prime is of order 1/sqrt(n) 

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