10⁹⁹⁹⁹⁹⁹ - 1087604 · 10²⁸⁷⁰⁰⁰ - 1

This prime's information:

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (12 Sep 2021):  (report abuse)

Currently, the 2nd largest known proven under-one-million-decimal digit prime. CHG proof is available at dropbox See also its sibling - the smallest known proven one-million-decimal digit prime. Also, a nearly repdigit prime (only 5 digits are different from the rest which are 999994 nines). Primality testing 10^999999-1087604*10^287000-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4, 16 threads on A 3321925-bit number Calling Brillhart-Lehmer-Selfridge with factored part 28.70% 10^999999-1087604*10^287000-1 is Lucas PRP! (55094.2968s+0.0278s) n=10^999999-1087604*10^287000-1; G=10^287000*4*29*359*479; F=1; Target "MS" has 999999 digits. Modulus provides 28.700758689553811534%. Right endpoint has 138978 digits. LLL[1, 1] for client 1 has [h, u] = [4, 1] and digits in [1, 16492] LLL[2, 1] for client 2 has [h, u] = [4, 1] and digits in [16492, 35666] LLL[3, 1] for client 3 has [h, u] = [5, 1] and digits in [35666, 61337] LLL[4, 1] for client 4 has [h, u] = [5, 1] and digits in [61337, 74172] LLL[5, 1] for client 5 has [h, u] = [5, 1] and digits in [74172, 80590] LLL[6, 1] for client 6 has [h, u] = [6, 2] and digits in [80590, 94078] LLL[7, 1] for client 7 has [h, u] = [6, 2] and digits in [94078, 104868] LLL[8, 1] for client 8 has [h, u] = [6, 2] and digits in [104868, 113500] LLL[9, 1] for client 9 has [h, u] = [6, 2] and digits in [113500, 120406] LLL[10, 1] for client 10 has [h, u] = [6, 2] and digits in [120406, 125931] LLL[11, 1] for client 11 has [h, u] = [6, 2] and digits in [125931, 130350] LLL[12, 1] for client 12 has [h, u] = [6, 2] and digits in [130350, 133886] LLL[13, 1] for client 13 has [h, u] = [6, 2] and digits in [133886, 136715] LLL[14, 1] for client 14 has [h, u] = [6, 2] and digits in [136715, 138978] LLL was split between 14 clients. ... Validated in 29 sec.

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.