Phi(3903, 10)
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: | Phi(3903, 10) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p44 : Broadhurst, OpenPFGW |
| Decimal Digits: | 2600 (log10 is 2599.9546770212) |
| Rank (*): | 100786 (digit rank is 1) |
| Entrance Rank (*): | 23861 |
| Currently on list? (*): | no |
| Submitted: | 2/5/2001 02:49:05 UTC |
| Last modified: | 2/4/2026 09:31:50 UTC |
| Database id: | 30341 |
| Status Flags: | none |
| Score (*): | 28.2548 (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.
User comments about this prime (disclaimer):
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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 30341 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper.php?id=1100000000032389036 -q"Phi(3903,10)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3903,10) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000032389036
Prime_Testing_Warning,
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 8637-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.82%
Phi(3903,10) is prime! (0.2171s+0.0055s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
17
41
53
67
79
101
131
251
271
521
859
1301
3541
5051
9091
21401
25601
27961
60101
77351
107251
200201
2311921
4271801
7019801
265371653
431684501
1058313049
82009322851
162503518711
182521213001
14103673319201
78875943472201
1680588011350901
4347195468174001
1031498834064949381
12763852652999774041
280672874149406424401
318942474614140390001
1900381976777332243781
12119730504567977254081
23098714167966114959599501
2737820036624672031089487008281
5538396997364024056286510640780600481
3733209604853765522511798189559871765401
8396862596258693901610602298557167100076327481
515598058349426893425512324539506997710608203280700351680904729473604464893512426851
16184717413009579260371945398681770...(114 digits)...43195331250705338664714884091786251
14176580788140166982612662932269638...(155 digits)...95571176996529118267301590082336151
99289375637786344255515599181595884...(206 digits)...15000933748377623448310239241465001
77636448947195236747133013143811675...(237 digits)...15756342052306072869338993143889701
59
83407
101467741modified 2026-02-04 09:31:50 created 2026-02-04 09:31:45 id 187672
field value prime_id 30341 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing Phi(3903,10) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 11 Running N-1 test using base 31 Running N+1 test using discriminant 43, base 1+sqrt(43) Calling N-1 BLS with factored part 2.81% and helper 0.30% (8.77% proof) Phi(3903,10) is Fermat and Lucas PRP! (117.070000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 20:19:16 id 61769
Query times: 0.0008 seconds to select prime, 0.0009 seconds to seek comments.
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