Primes are NOT infinite...41 million digits...the largest ever found, not exactly but roughly in that vicinity....printed on 8.5 by 11, paper............a prime of 10 000 digits is approx 3 pages long..............so..........41,000,000/10,000 = 4,100................so to print that number out, on 8 and a half sheet, by ll, standard printer paper............4,100 x 3 = 12,300 pages long......an entire encyclopedia set.

I bet the last prime is about 80 million, roughly twice the largest found............24,600 pages.......or so.........80 x 10^6.........1.618.......6.28..........168 less than 1,000............68 %, the pattern persists, up the number line..

80 million can be written as 2^3 x 10^7..........2^3 = 8....237........80 million rewritten .....7 and 8. 1/4 pi = 0.78..............music.....a - g, 7 musical notes.....8..octaves, double up, 1/2 down.........18281828, 3 - 10 of e...........3 and 1.....pi and infinity, together they produce waves

.....like 138,  67 + 71 = 138....2.7^5 = 138, like 2pi.........b/c 57 degrees is 1 pi rad....5 + 7 = 12.....last 3, 1st 3 of e...12, sum of five and seven, 75% and 57 degrees, 1 pi rad, spun, like pi, spin in quantum physics, vortex, the weather, nature.........12 and 31 or 1/3 ......music, harmonic series, 1/2 + 1/3, 1st 2 fractions, 1/2 again, chaos, king chaos, creator of the universe, ancient China.....not in the same order, 2.71....

 1 and 2.........1/2 line.......137  ... 138, differ in 7 and 8.......music......end digits of the two dist 0 - 9 with exactly 3.....41, 43, 47......137.........71, 73, 79........139, avg 138..........e to the 5th......2.7^5..........again like 2 pi.....3/4 = 0.75.....spin 3/4......43, take out the division symbol, 43, the 14th prime, 14i..........37 to 73..............37/36, the 12 th in Eulers product,....12th prime into the 21st, 12 + 21 = 33.....infinity and two 3s........fractals......chaos........matches in at least two ways.......- 2, 0.........20, 1, 3, 7, 9.............only 4 options for an end digit of primes greater than 10........they sum to 20........- 2, 0.......not so trivial after all.

Largest Known Prime Number: 2^136,279,841-1

BLOWING ROCK, NC, October 21, 2024 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^136,279,841-1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th.

Luke is currently GIMPS' most prolific contributor. He is joined by thousands of volunteers using free GIMPS software available at www.mersenne.org/download/.

The new prime number, also known as M136279841, is calculated by multiplying together 136,279,841 twos, and then subtracting 1. It is over 16 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 18 Mersenne primes. Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell founded an authoritative web site on the largest known primes which is now maintained by volunteers, and has an excellent history of Mersenne primes.

Rise of the GPU

This prime ends the 28-year reign of ordinary personal computers finding these huge prime numbers. In 2017, Mihai Preda saw the ever increasing power of GPUs in PCs and wrote the GpuOwl program to test Mersenne numbers for primality, making his software available to all GIMPS users.

Luke Durant, a 36 year-old researcher and former NVIDIA employee, also understands the power of the GPUs he helped design. Luke decided that finding a new Mersenne prime would be a great demonstration that GPUs can be used for more than AI. GPUs are well suited to fundamental math and science research as well.

Luke began contributing to GIMPS in October 2023, and believed the explosive growth of GPU availability in the cloud presented a unique opportunity for the software developed by Mihai. Luke developed infrastructure to run and maintain a suite of GIMPS software across many GPU servers. At time of discovery, Luke's "cloud supercomputer" was comprised of thousands of server GPUs, spanning 24 datacenter regions over 17 countries.

After nearly a year of testing, Luke finally struck paydirt. On October 11, an NVIDIA A100 GPU in Dublin, Ireland, reported that M136279841 is probably prime. On October 12, an NVIDIA H100 in San Antonio, Texas, USA, confirmed primality with a Lucas-Lehmer test.