Phi(2137, - 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(2137, - 10) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique, ECPP |
| Proof-code(s): (*): | c6 : Larrosa, Primo |
| Decimal Digits: | 2136 (log10 is 2135.9586073148) |
| Rank (*): | 107860 (digit rank is 5) |
| Entrance Rank (*): | 27074 |
| Currently on list? (*): | no |
| Submitted: | 12/14/2000 00:01:18 UTC |
| Last modified: | 2/4/2026 10:05:01 UTC |
| Database id: | 34195 |
| Status Flags: | none |
| Score (*): | 27.6422 (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.
- Unique (archivable *)
- Prime on list: no, rank 44
Subcategory: "Unique"
(archival tag id 210423, tag last modified 2025-08-23 01:37:16)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 928
Subcategory: "ECPP"
(archival tag id 210422, tag last modified 2026-01-31 06:37:12)
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 34195 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000013337158.txt -q"Phi(2137,-10)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(2137,-10) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000013337158.txt
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 7099-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.95%
Phi(2137,-10) is prime! (0.1570s+0.0048s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
13
37
73
101
137
179
1069
2137
9613
9901
38449
138841
158777
497867
3154339
99990001
103733951
104984505733
118941438655807
540913940517169
12147237304901893
118638175449391414217
5078554966026315671444089
205634535002357125750465106981645977
403513310222809053284932818475878953159
833845535443385228657693694666672878355349
1054927415257693631440903203309586374903030044747807503
4180967272673252032291190917188955510245874180001164839931077197586653
27764795309426312955779180075843706...(102 digits)...95477739802212252078988231259971169
17325664671184692265593556093236354...(158 digits)...74754110413766826738528679977268603
18547092770394661955046893866403953...(167 digits)...21812682716262365263155956618360389
23
43
9421829modified 2026-02-04 10:05:01 created 2026-02-04 10:04:56 id 187679
field value prime_id 34195 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 2 Primality testing Phi(2137,-10) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 3+sqrt(7) Calling N-1 BLS with factored part 2.30% and helper 0.16% (7.08% proof) Phi(2137,-10) is Fermat and Lucas PRP! (104.750000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 18:49:48 id 61597
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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