primV(11221)
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: | primV(11221) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 2002 (log10 is 2001.2651275499) |
| Rank (*): | 111008 (digit rank is 27) |
| Entrance Rank (*): | 10051 |
| Currently on list? (*): | no |
| Submitted: | 10/1996 |
| Last modified: | 2/4/2026 10:09:05 UTC |
| Database id: | 37347 |
| Status Flags: | none |
| Score (*): | 27.4391 (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.
- Lucas primitive part (archivable *)
- Prime on list: no, rank 116
Subcategory: "Lucas primitive part"
(archival tag id 195689, tag last modified 2024-10-11 22:37:11)
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 37347 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 1841312705...6184977201 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000306382844.txt
trial
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6649-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6649-bit number
Running N+1 test using discriminant 31, base 10+sqrt(31)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6649-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 6728/6810 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 31, base 10+sqrt(31)
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 6649-bit number
Calling N-1 BLS with factored part 34.63% and helper 1.07% (104.98% proof)
1841312705...6184977201 is prime! (0.7572s+0.0006s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
29
37
71
83
113
139
179
211
227
229
281
421
461
797
911
1151
1289
1381
1427
3221
3457
5981
8693
9349
14503
26449
28657
28729
30323
42293
54833
95419
141961
229223
324301
519499
686551
978347
1917511
4483163
29134601
164967041
186313849
212067587
742652831
3336915203
10694421739
30762400411
460289405267
486077598803
561434197549
2152958650459
351301301942501
2441738887963981
965840862268529759
253860154307738955341
2608509549583653221689
252171167457207277136719
612606107755058997065597
8644318392628731293362631
461260622582580115020470322214561
1059009573400125529504166094598642626708730201
5260841010529855006081292996380789834608128418946685161
55178337066529867890457879347065097397315177033672963849
660197807808925399815745309795984424904274580236856941016852839261
2591
3637
6926111
19311289modified 2026-02-04 10:09:05 created 2026-02-04 10:08:55 id 187680
field value prime_id 37347 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 17 Primality testing primV(11221) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Calling Brillhart-Lehmer-Selfridge with factored part 6.41% primV(11221) is PRP! (22.770000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:30:27 id 63909
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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