(10499 + 2919433)6 + (10499 + 2919433)3 + 1
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
| Description: | (10499 + 2919433)6 + (10499 + 2919433)3 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 2995 (log10 is 2994) |
| Rank (*): | 100128 (digit rank is 2) |
| Entrance Rank (*): | 21708 |
| Currently on list? (*): | no |
| Submitted: | 10/11/2000 00:23:50 UTC |
| Last modified: | 2/4/2026 07:51:53 UTC |
| Database id: | 29729 |
| Status Flags: | none |
| Score (*): | 28.6942 (normalized score 0) |
Archival tags:
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Generalized Unique (archivable *)
- Prime on list: no, rank 1570
Subcategory: "Generalized Unique"
(archival tag id 225614, tag last modified 2026-01-09 22:37:30)
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.
field value prime_id 29729 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (10^499+2919433)^6+(10^499+2919433)^3+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000007611178264
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9946-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 49.99%
(10^499+2919433)^6+(10^499+2919433)^3+1 is prime! (0.1189s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
11
31
9099810079
62538454541419
72851820754793074843
10000000000000000000000000000000000...(500 digits)...00000000000000000000000000002919433
1093
258329
19236053modified 2026-02-04 07:51:53 created 2026-02-04 07:51:48 id 187663
field value prime_id 29729 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"Phi(3,(10^499+2919433)^3)" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 776270 Running N-1 test using base 2 Primality testing Phi(3,(10^499+2919433)^3) [N-1/N+1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 19900 bit request FFT size=(1280,16) Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 19900 bit request FFT size=(1280,16) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 19900 bit request FFT size=(1280,16) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 19908 bit request FFT size=(1280,16) Calling N+1 BLS with factored part 0.30% and helper 0.12% (1.03% proof) Phi(3,(10^499+2919433)^3) is Fermat and Lucas PRP! (8.0400s+0.0100s) modified 2020-07-07 22:30:47 created 2003-10-04 06:22:28 id 71371
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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