Phi(211, - 30528476176)
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, - 30528476176) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | DB : Dubner, Brent, Cruncher |
| Decimal Digits: | 2202 (log10 is 2201.788076691) |
| Rank (*): | 107487 (digit rank is 1) |
| Entrance Rank (*): | 6701 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 10:00:59 UTC |
| Database id: | 33783 |
| Status Flags: | none |
| Score (*): | 27.7368 (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 1577
Subcategory: "Generalized Unique"
(archival tag id 225621, 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 33783 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000001984954385.txt -q"Phi(211,-30528476176)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(211,-30528476176) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001984954385.txt
Prime_Testing_Warning,
Running N-1 test using base 23
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 7315-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 36.25%
Phi(211,-30528476176) is prime! (0.2324s+0.0081s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
29
31
37
41
43
61
71
79
101
139
181
211
241
281
337
379
419
421
601
673
739
881
2311
2521
10501
20749
50723
66571
83203
223441
276151
318641
777001
1183561
1339711
1581553
2765281
9770251
12120391
13895449
19551967
44308181
53725421
128001301
213101857
615467681
7386669281
24805530457
27806136121
30601685951
104909548409
191504430391
906410738381
1003061263681
1902698765353
77078163638461
172746533302477
655460821256641
693999104535241
1566300930175171
5346848976102943
7431829446294961
86251842807133669
105562540957761889
31389749771766311297
569453608570112635601
5909040269993370471991
21589554936895106463065233
1741676511404832240722917567
418495472901964515933623219081
25745653786895229615966097211472101
733888128063272308555220462835521641
37496184117100248577182368981103321697
1445268449324362492608833867000108215501
3172782936471902278362747848324969226862121
24025871665574700683559660222234684341008664677120681
754468334374469076605427853754024225575690313462250408675376646999652640918445917201
32011603793090011670737516505816860...(96 digits)...21966531221305172099514103747061751
11116928088159214452007580177377353...(105 digits)...29877022420089447308769855844971761
34442247945570902448086704038366019...(114 digits)...46887664015329011081446731041416617
72602937795485931210099217861160021...(239 digits)...71355446905234289447221861688629441
13477874064253634929589366556696824...(247 digits)...73759557569866352677315368973534561
173
5252347modified 2026-02-04 10:00:59 created 2026-02-04 10:00:53 id 187677
field value prime_id 33783 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 23 Primality testing Phi(211,-30528476176) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 47 Running N-1 test using base 53 Running N-1 test using base 59 Running N+1 test using discriminant 73, base 2+sqrt(73) Calling N-1 BLS with factored part 5.13% and helper 0.11% (15.52% proof) Phi(211,-30528476176) is Fermat and Lucas PRP! (93.700000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 19:17:58 id 61647
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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