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Old 2021-08-23, 15:08   #1
Nov 2020
Massachusetts, USA

52 Posts
Default 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.

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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Old 2021-08-27, 10:12   #2
bur's Avatar
Aug 2020

6418 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.
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