My computer can do it in a quarter of that time. In fact, it can do it in a tenth of that time. In fact, it can do it in an infinite-small fraction of that time.

[CODE]? floor((31.4*10^12/10^4)^4)
97211712160000000000000000000000000000
[/CODE]

This is the number of core years to prove a 31.4 trillion digit number with Primo. Of course you would need to have a great big system, be prepared to backtrack over millenia, and expect Marcel (and decendants-of-Marcel) to build the tables. If you can use enough atoms to store the step information and the certificate without creating a black hole you will be doing well :grin:

[QUOTE=LaurV;511314]My computer can do it in a quarter of that time. In fact, it can do it in a tenth of that time. In fact, it can do it in an infinite-small fraction of that time.[/QUOTE]

Ha ha.

(Although an "infinite-small fraction" of an infinite time span
might be infinite or finite itself.)

Using GMP, assuming it all fits in memory and GMP scales fine, it's only 1.8 billion years to finish BPSW.

My single threaded Primo calculation came out to only exp( 4.01 * (log(3140000000000)-log(2000)) + log(2313.8) ) / 60 / 60 / 24 / 365.25 = 550528055283376774128261550300497 years. Based on timings from a few years ago to compute various sizes up to 2000 digits, and assuming of course that we can just handwave practicality and scaling.

AKS using Bernstein Theorem 4.1, about 5e59 years. But parallelism is trivial, so that will really help a lot. :cool:

[QUOTE=J F;483844]#20 at 833K digits atm, no PRP.
Quick (and very rough) approximation that a random pick
with n decimal digits is prime: 1 : 2.3n
Chance to find none between 750K and 1M is around 90%.[/QUOTE]

Any updates on this search?

What is the status of a(20)? Will it reach 10^6 soon?

[QUOTE=davar55;553818]What is the status of a(20)? Will it reach 10^6 soon?[/QUOTE]

With no activity since March of 2018, I suspect the user gave up.

Oh I see. I thought of a different possibility.