Phi(211, - 136326383940321)
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(211, - 136326383940321) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | D : Dubner, Cruncher |
| Decimal Digits: | 2969 (log10 is 2968.261782191) |
| Rank (*): | 100260 (digit rank is 2) |
| Entrance Rank (*): | 3264 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 07:49:14 UTC |
| Database id: | 29765 |
| Status Flags: | none |
| Score (*): | 28.6674 (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 1572
Subcategory: "Generalized Unique"
(archival tag id 225616, 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 29765 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 Phi(211,-136326383940321) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002385071898
Prime_Testing_Warning,
Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9861-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.66%
Phi(211,-136326383940321) is prime! (0.3195s+0.0060s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
29
31
43
61
67
71
97
101
181
197
211
229
281
337
421
491
631
673
757
1597
1709
2857
3361
4621
5749
7309
11257
12037
15791
26041
46901
68713
79621
129529
161881
412051
422101
563249
823261
931421
2143501
3182761
3620681
7229951
7798201
7965421
11679307
30068321
51085651
74448601
85501951
118513249
121392181
370271329
2650364711
153533100239
255676371889
270220209841
600395118863
3902214461881
11514472407271
15078335156641
18309995701201
91842879190021
313289647401161
1015310009268241
456500014519911601
924697479295361521
980565695359896661
3469153916826144241
8050344741784101271
86448400891774309879
681775523321614484197
1417274520868860246954131
49091940520768088494358809
24514725095087896937865269009
207037923687717470300196070921
46448579708291472249632699462101
100964238716132941535541795947161
458746188096575976379933538345161
7085269284588592835888510375140721
45566849188458608245385202737476541
696775096100916552186026060011722121
995008167940722624539213579577313036321
32837098756270588148079507464984918383970087048753191001
345397874571618711127677302429067634309129130931422754241
184052393092027812350589569938472716009414483729712629073900448461
1835049063167920288842462305237388190280163453848267435099299010646849449758513
28303133905669331685983023150969563312797893715216476606462275077888055109091761
26870518380017718891850054391672397...(152 digits)...97477294156859239427504854777465851
36604654855172801565080399807012076...(166 digits)...53053380395728505274582702851804553
53
2915369
3457991modified 2026-02-04 07:49:14 created 2026-02-04 07:49:09 id 187662
field value prime_id 29765 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 19 Primality testing Phi(211,-136326383940321) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 41, base 8+sqrt(41) Calling N-1 BLS with factored part 4.86% and helper 0.06% (14.65% proof) Phi(211,-136326383940321) is Fermat and Lucas PRP! (120.890000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:24:12 id 61850
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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