Phi(5403, 2)
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(5403, 2) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | c5 : Carmody, Primo |
| Decimal Digits: | 1084 (log10 is 1083.7079843903) |
| Rank (*): | 127595 (digit rank is 11) |
| Entrance Rank (*): | 46455 |
| Currently on list? (*): | no |
| Submitted: | 3/6/2001 17:27:56 UTC |
| Last modified: | 2/4/2026 10:42:14 UTC |
| Database id: | 53174 |
| Status Flags: | none |
| Score (*): | 25.5234 (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 1582
Subcategory: "Generalized Unique"
(archival tag id 225626, 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 53174 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000000185517.txt -q"Phi(5403,2)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(5403,2) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000000185517.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3603-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.40%
Phi(5403,2) is prime! (0.0420s+0.0064s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
13
17
19
31
37
41
61
73
101
109
151
181
241
251
331
401
433
601
631
1201
1321
1801
4051
8101
23311
38737
54001
61681
63901
100801
115201
268501
340801
617401
695701
2787601
10567201
13334701
18837001
29247661
1182468601
1348206751
3173389601
4562284561
4714696801
168692292721
1133836730401
307116398490301
413150254353901
6269989892198401
13861369826299351
469775495062434961
3192261504216112476901
281941472953710177758647201
5807380901690048305970962748462547129404401
1461503031127477825099979369543473122548042956801
53754844105498735271643180473054106...(102 digits)...16474824881955502486161902175946001modified 2026-02-04 10:42:14 created 2026-02-04 10:42:09 id 187711
field value prime_id 53174 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(5403,2) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 8.70% and helper 0.08% (26.23% proof) Phi(5403,2) is Fermat and Lucas PRP! (15.110000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:49:19 id 60870
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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