Phi(211, - 11662935330816)
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, - 11662935330816) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | D : Dubner, Cruncher |
| Decimal Digits: | 2745 (log10 is 2744.0296521826) |
| Rank (*): | 100525 (digit rank is 1) |
| Entrance Rank (*): | 3459 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 08:58:24 UTC |
| Database id: | 30069 |
| Status Flags: | none |
| Score (*): | 28.4228 (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 1574
Subcategory: "Generalized Unique"
(archival tag id 225618, 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 30069 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper.php?id=1100000002467761748 -q"Phi(211,-11662935330816)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(211,-11662935330816) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002467761748
Prime_Testing_Warning,
Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9116-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 34.13%
Phi(211,-11662935330816) is prime! (0.2480s+0.0049s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
29
31
43
61
71
211
241
281
421
1847
4621
6551
7351
19441
20749
21701
23581
56197
58057
192193
234721
402949
614041
683021
823201
1459921
1682311
3413257
3416953
6337561
6725881
15452893
42489521
139687787
403542553
576966601
1657019701
1781292911
9430380961
13449304021
16859251249
143279211041
221977910449
285291239339
11656627631881
12460371984481
27151982816641
58379851720681
166024785090221
2757557575481801
10922246800901941
15311497441001791
47110461724155481
60652187654369221
7691595405134080441
13192561009584531233
39808595652147328777
189994792596885844121
225579884313293234311
55964674130653303390831
613863482523871108665361
2374711071039162249535681
136024060530784456423895041
136097666602592166032345401
889627300458826741440628609
3691206347734762749586121291921
2636503224699651592601042830982537
3558605116874802726643605048310441
13413990677472189906062786684365801
261931984105167918634863115235691307987789
78827821299688141312009209089861696808136515361
10624057605097857440272689469488109453314870380513848226801
23133882607041849746563653719824263...(97 digits)...66261612393108057056750836629991481
13687381274073486089471117597406998...(126 digits)...79740437035775433815649796771507941
13452782511036035934233565037761377...(141 digits)...34739051262694333747756861466577441
76946438144483818010181498743702400...(151 digits)...84423196282667945154940295765894241
76581264669803059577252476058516427...(278 digits)...87524751971381697532131053961960161
809
3172649modified 2026-02-04 08:58:24 created 2026-02-04 08:58:19 id 187668
field value prime_id 30069 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,-11662935330816) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 37, base 18+sqrt(37) Calling N-1 BLS with factored part 3.81% and helper 0.11% (11.54% proof) Phi(211,-11662935330816) is Fermat and Lucas PRP! (78.180000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 20:43:29 id 61803
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.