Phi(211, - 107503718560000)
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, - 107503718560000) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | D : Dubner, Cruncher |
| Decimal Digits: | 2947 (log10 is 2946.5989322245) |
| Rank (*): | 100211 (digit rank is 1) |
| Entrance Rank (*): | 3273 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 08:49:18 UTC |
| Database id: | 29786 |
| Status Flags: | none |
| Score (*): | 28.6446 (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 1573
Subcategory: "Generalized Unique"
(archival tag id 225617, 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 29786 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,-107503718560000) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002344745885
Prime_Testing_Warning,
Running N-1 test using base 47
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9789-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.63%
Phi(211,-107503718560000) is prime! (0.3629s+0.0048s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
23
29
31
37
41
43
61
71
73
113
197
211
241
281
337
367
421
463
757
967
1321
2377
3221
3571
3613
3643
4651
4801
7309
13241
17921
21701
42281
51721
85093
96181
129361
222601
913417
1630801
2009881
2426131
3090011
4830281
7241977
10368401
21025201
23802001
29785201
65920801
114959041
421554379
2204457601
7265009627
43667673701
84086801681
522756962281
979688771531
1192217873617
40537149423457
109683516401941
6097877201000719
12868922554826311
213433291094791587961
1114987825028382379621
2324170660361859472381
269234530736083522742287
712211112541473932392321
1986739420411475729080537
3374078091900301040948281
4862031764504661745848313
11557048389586240459804191601
11560638649690185325611995221
9241311472610708810476581921533
68519392651521851412951213000373
5258986066694495045010272638625289525905281
168366270832192018413385867480778546674065451
6134017067231731613669923467553219916544531605461
210239042892943776745619400917180104032508513457676082787551
1417477591779429409713864134785785037350472753149115522127210437609
5020872185078229257137984268716108740917231315984011011671879715534503635489
42216030335459784533728189283107471...(99 digits)...69364507209208462776987486892963321
54565963331098291279414984032788258...(158 digits)...09653567190617829312141681966304701
1373
16553
2509424881modified 2026-02-04 08:49:18 created 2026-02-04 08:49:13 id 187666
field value prime_id 29786 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 47 Primality testing Phi(211,-107503718560000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 59 Running N+1 test using discriminant 79, base 16+sqrt(79) Calling N-1 BLS with factored part 4.50% and helper 0.26% (13.74% proof) Phi(211,-107503718560000) is Fermat and Lucas PRP! (103.010000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:18:16 id 61844
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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