New ECPP record (currently: 73,269 digits)

[paulunderwood]

Originally Posted by frmky

I am aware this will soon be exceeded, but 104824^5+5^104824, at 73,269 digits, is prime. Stage 1 took 32 days on 20 24-core computers using GWNUM. Stage 2 took 27 days on 8 20-core computers. A few steps with large prime factors of h took most of the time in stage 2. I will explore the effects of further limiting the largest prime factor of h. Thanks again to Andreas for creating CM and Paul for adding support for GWNUM.

Originally Posted by xilman

Nice work!

Any estimate when the first 100K digit prime will be proven?

Congrats Greg!

R109297 should be doable with 4x the resources Greg used

[rudy235]

So now we have a 73,269 digit proven via ECPP. this is a Leyland Prime. One that cannot be proven by specifically tailored methods.

The prime in question is 5¹⁰⁴⁸²⁴ + 104824⁵ 73269 digits.

A couple of things are worth noting:

The “gap” in digits to the next ECPP primes is notable. Over 23000 digits more than the one just discovered only 2 months ago. The largest 8 ECPP primes have been discovered in the past 52 weeks.

We can only assume that R86453 will be proven prime in the fairly near future as it is only twice as hard as this one just discovered.

Huge congratulation to Greg Childers.

[kruoli]

Originally Posted by xilman

Any estimate when the first 100K digit prime will be proven?

Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered.

In the former, that should be 10^99,999+309,403, if my quick calculations are correct.

[xilman]

Originally Posted by kruoli

Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered.

In the former, thed should be 10^99,999+10^99999+309403, if my quick calculations are correct.

Fixing a minor tyypo: I believe you mean


In the former, that should be 10^99,999+309403, if my quick calculations are correct.

[kruoli]

Wow, I have no clue how that happened. :D

1068

[paulunderwood]

Comparing total CPU hours for Greg's recent proof with Andreas's expected proof of R86453, the minimal 100k digit number and R109297:

? (86453/73269.)^4
1.9383813225131506029336873744208292121                          
? (100000/73269.)^4
3.4699158544965667114008777645966191866                          
? (109297/73269.)^4
4.9516724586074826088662323174646459749

But I wonder if Andreas uses GWNUM, which will skew the stats.

[JeppeSN]

Originally Posted by kruoli

Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered.

In the former, that should be 10^99,999+309,403, if my quick calculations are correct.

The smallest PRP with 100'000 digits is registered but not proven prime (I think). The first prime with exactly 100'000 digits that was proven (but not with ECPP) could be 593573509*2^332162+1 from 16 August 2000.

However, given the context of the thread, it is virtually certain xilman meant the first prime with at least 100'000 digits proven prime with the ECPP method.

/JeppeSN

[xilman]

Originally Posted by JeppeSN

However, given the context of the thread, it is virtually certain xilman meant the first prime with at least 100'000 digits proven prime with the ECPP method.

Correct.