Happy weekend for Five or Bust project

Raydex · 2021-08-23, 15:08

On Saturday, August 21, the Five or Bust project has reached a new milestone in the quest to find a prime for the multiplier k = 22699.

https://www.primegrid.com/stats_sob_llr.php

22699 has become the first of the five multipliers to exceed an exponent of 35 million (35,000,000). In fact, it is now considerably far above 35 million while the other four are still in the 34****** range. The exponent as of late is 35,438,302, more than 500,000 numbers higher than the next highest exponent: 34,898,787 for k = 67607.

It has been nearly five years (half a decade) since the discovery of a prime number for k = 10223 on Halloween of 2016, but let's keep working to (hopefully) find primes for the remaining five. If found, it will make history as it will be the first non-Mersenne prime number with over 10 million digits to be discovered. On this day in 2008, the Mersenne prime M(43112609) became our first known 10 million digit prime and its discoverer won an award for it when the prime was verified and made public in September of that year. As that prime enters its teen years today, let's do like we do any other day: to keep the spirit alive in finding the Proth primes for the remaining five multipliers!

bur · 2021-08-27, 10:12

With the mix of exponentially decreasing prime density and exponentially increasing computation times I guess the project will still be running in 2040. The question is, what'll be first, the next Mersenne prime or the next k eliminated from Five or Bust?

Another project with a chance of finding a 10,000,000+ digit prime is the generalized fermat search at Primegrid. b^2^21 has a leading edge b of 703,000, i.e. more than 12,000,000 digits. Not to mention the b^2^22 search with b of around 940,000 that - with more than 25,000,000 digits - would yield the largest known prime if successfull. That's a big if though.

HermannSW · 2023-08-11, 20:41

Quote:

Originally Posted by Raydex

It has been nearly five years (half a decade) since the discovery of a prime number for k = 10223 ...

In the official announcement from 2016 for that number
http://www.primegrid.com/download/SOB-31172165.pdf
the 4C computer proving that number prime the first time did need more than 8 days.
And the verifying 4C computer did need more than 27 days ...

Compute power gets better and better — my new AMD 6C/12T 7600X CPU PC did prove it prime in 10.45:01h(!):
https://github.com/Hermann-SW/RSA_nu...hat-is-1-mod-4

I patched LLR software to write out 2nd last computed value which is "sqrt(-1) (mod p)" for the 9,383,761-digit prime p=10223*2^31172165+1, and used that to compute unique sum of squares for that prime in 2.9s only:
https://pari.math.u-bordeaux.fr/arch.../msg00002.html

P.S:
PC is currently proving Generalized Unique 11,887,192-digit prime Phi(3,-465859^1048576) with expected runtime of 6.72 days
(also for determining "sqrt(-1) (mod p)" and then sum of squares from that):
https://mersenneforum.org/showthread...984#post635984

Current state:

Code:

pi@pi400-64:~ $ ssh hermann@7600x uptime
 22:47:13 up 1 day, 13:34,  0 users,  load average: 4.95, 4.58, 4.45
pi@pi400-64:~ $ ssh hermann@7600x 'sed "s/^M/\n/g" nohup.out | tail -3'
465859^2097152-465859^1048576+1, bit: 9160000 / 39488394 [23.19%].  Time per bit: 14.503 ms.
465859^2097152-465859^1048576+1, bit: 9170000 / 39488394 [23.22%].  Time per bit: 14.530 ms.
465859^2097152-465859^1048576+1, bit: 9180000 / 39488394 [23.24%].  Time per bit: 14.505 ms.
pi@pi400-64:~ $

2021-08-23, 15:08	#1
Raydex Nov 2020 Massachusetts, USA 29 Posts	Happy weekend for Five or Bust project On Saturday, August 21, the Five or Bust project has reached a new milestone in the quest to find a prime for the multiplier k = 22699. https://www.primegrid.com/stats_sob_llr.php 22699 has become the first of the five multipliers to exceed an exponent of 35 million (35,000,000). In fact, it is now considerably far above 35 million while the other four are still in the 34**** range. The exponent as of late is 35,438,302, more than 500,000 numbers higher than the next highest exponent: 34,898,787** for k = 67607. It has been nearly five years (half a decade) since the discovery of a prime number for k = 10223 on Halloween of 2016, but let's keep working to (hopefully) find primes for the remaining five. If found, it will make history as it will be the first non-Mersenne prime number with over 10 million digits to be discovered. On this day in 2008, the Mersenne prime M(43112609) became our first known 10 million digit prime and its discoverer won an award for it when the prime was verified and made public in September of that year. As that prime enters its teen years today, let's do like we do any other day: to keep the spirit alive in finding the Proth primes for the remaining five multipliers!

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2021-08-27, 10:12	#2
bur Aug 2020 796581e-4;32539e-3 3×263 Posts	With the mix of exponentially decreasing prime density and exponentially increasing computation times I guess the project will still be running in 2040. The question is, what'll be first, the next Mersenne prime or the next k eliminated from Five or Bust? Another project with a chance of finding a 10,000,000+ digit prime is the generalized fermat search at Primegrid. b^2^21 has a leading edge b of 703,000, i.e. more than 12,000,000 digits. Not to mention the b^2^22 search with b of around 940,000 that - with more than 25,000,000 digits - would yield the largest known prime if successfull. That's a big if though.