Phi(211, - 37480960000)
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, - 37480960000) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | DB : Dubner, Brent, Cruncher |
| Decimal Digits: | 2221 (log10 is 2220.5002482484) |
| Rank (*): | 107130 (digit rank is 7) |
| Entrance Rank (*): | 6422 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 09:59:56 UTC |
| Database id: | 33492 |
| Status Flags: | none |
| Score (*): | 27.7632 (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 1576
Subcategory: "Generalized Unique"
(archival tag id 225620, 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 33492 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000002004819228.txt -q"Phi(211,-37480960000)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(211,-37480960000) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002004819228.txt
Prime_Testing_Warning,
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 7377-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 37.62%
Phi(211,-37480960000) is prime! (0.1610s+0.0057s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
29
31
41
43
61
67
71
101
211
229
239
281
337
401
421
439
757
1801
2521
3181
3931
6301
8443
8761
9871
10193
19531
52501
146953
175291
184321
193601
376501
927541
5064907
6127321
8061481
12590113
29945833
39712471
41094523
526703791
914621821
3498904459
3604205333
4133701937
8978490061
12060099941
138857703181
869942744521
3726179747761
4880568496021
80658031016921
379261893841573
8032443902362651
9559671204290617
20411017986125341
54078794920444321
124681597191348961
2205777607229586601
6188698271472925433
128435638152802642621
2972050151817034735441
13764190375357235624959
16415374651007311740251
29729771229286229612449
585499195391014869171601
1117984295710892581902421
3619006554719766248434257457
156242785770246349140905711473
41076403767192971816231647929440651
5241781732512646299682156583380667101
1651791379482306973285702305241677004646441
1785235621559334340578004794655498199835017058241
7310166513091292816800835137336114362457535689837
69493743743108019056176992922762046...(99 digits)...60249179910956691662467487221268171
37409181537423317274836997306602892...(112 digits)...43625287794167327611021915346186361
76864971651973056819834415682809205...(127 digits)...10460653872912755851264037480960001
77040061797116039846546793266625303...(127 digits)...18543968719057603251474975641794041
12722132662414710079525095842379740...(209 digits)...15461665100114641436950531112859161
43301112114045158219179200929722376...(501 digits)...80257309956017637540670854693136921
73
593modified 2026-02-04 09:59:56 created 2026-02-04 09:59:51 id 187676
field value prime_id 33492 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 17 Primality testing Phi(211,-37480960000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 5.52% and helper 0.22% (16.77% proof) Phi(211,-37480960000) is Fermat and Lucas PRP! (59.180000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 19:19:39 id 61649
Query times: 0.0236 seconds to select prime, 0.015 seconds to seek comments.
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