20170322, 03:32  #188 
May 2004
New York City
2^{3}×23^{2} Posts 
Actually I consider the work put into this sequence and the discovery
of the a(20) prime very valuable. Perhaps my expectations for an "important result" were already sufficiently satisfied. It certainly is a very interesting anomalously large prime. 
20170325, 09:44  #189 
Sep 2013
56_{10} Posts 
What is 'anomalously large'? You can approximate the probability
that the sequence from a starting value will yield no prime up to some digit count. The chance to 'survive' to 300K digits is order of magnitude 0.5%. I got 11 >300K with the smallish sample size of 1666, so far that seems sane enough to me. 
20170519, 13:34  #190 
May 2004
New York City
1088_{16} Posts 
Is a(20) longer than 613373?

20170520, 06:27  #191 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
47·197 Posts 

20170523, 13:23  #192 
May 2004
New York City
2^{3}×23^{2} Posts 

20170626, 15:05  #193 
May 2004
New York City
2^{3}×23^{2} Posts 
Actually, is a(20) well defined until or unless a prime is found at that location?
So the previous post was just a request for a progress report. 
20170626, 22:12  #194 
Sep 2013
2^{3}×7 Posts 
Progress report: #20 somewhere around 750K digits, no PRP yet

20170627, 13:25  #195 
May 2004
New York City
1000010001000_{2} Posts 
Thanks. Great work. This result is surprisingly tantalizing.

20170627, 15:48  #196 
Einyen
Dec 2003
Denmark
3×17×59 Posts 
I stopped at 750k digits searching for "standard" pi primes starting at 3.1415. No new primes before or after the 613373 digit one.

20170627, 16:25  #197 
"Mark"
Apr 2003
Between here and the
2^{2}·23·67 Posts 

20170627, 16:33  #198 
Einyen
Dec 2003
Denmark
3·17·59 Posts 
Yes, I sieved up to 1 million digits, and I have actually still been sieving sometimes on computers at work. I'm on vacation now, I will try to sort out how far I got and post in 12 weeks.

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