(4332612041 - 1)/43325
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: | (4332612041 - 1)/43325 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p170 : Wu_T, Primo, OpenPFGW |
| Decimal Digits: | 55827 (log10 is 55826.453098379) |
| Rank (*): | 60071 (digit rank is 1) |
| Entrance Rank (*): | 49242 |
| Currently on list? (*): | yes |
| Submitted: | 11/21/2017 18:54:12 UTC |
| Last modified: | 11/22/2024 08:53:19 UTC |
| Database id: | 124011 |
| Status Flags: | none |
| Score (*): | 37.7571 (normalized score 0.0005) |
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 Repunit (archivable *)
- Prime on list: yes, rank 17
Subcategory: "Generalized Repunit"
(archival tag id 218934, tag last modified 2025-01-20 23:37:21)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 124011 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000001067109879 -q"(43326^12041-1)/43325" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (43326^12041-1)/43325 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000001067109879
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 185452-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 185452-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 185452-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 142/185503 ERROR: ROUND OFF 0.49642>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 20K on A 185452-bit number
Calling N-1 BLS with factored part 35.60% and helper 0.02% (106.81% proof)
(43326^12041-1)/43325 is prime! (198.8317s+0.0004s)
[Elapsed time: 3.33 minutes]
Helper File:
2
3
5
11
29
37
41
71
83
97
173
197
211
233
281
421
431
541
743
1171
1291
1721
3011
3061
3347
4129
5881
6301
12041
13417
27091
43541
106801
120401
231169
250433
637691
1021001
1752481
9528641
9615257
15921511
51410113
52602761
65597017
88963817
89436481
102494881
112029191
209781731
1902777521
2379914321
3736294769
3747112021
4058292841
6427358953
7757765881
18544608281
27033363701
50510186329
111723754591
8907282223421
9629316450161
19891711470569
36020315500261
74336116173509
183365728603121
224265080405521
264429655894783
274771793410031
276615253999883
1348132947346151
10166266248104737
18960845594403611
102545361470375081
195647003758491601
2619924398471762321
621519518171086451677
3195643024324628217397
219985663522268447777023
567291842660159008597529
848968175090988721147661
3223760938510300988220401
3687542197537162830501821
6614569686845255157343481707
31473233272806818216106627131
1128547390412780788165737160721
81970987247566981291317882478061
617938582949000716260797410008581
35653885930109533339847985232081491521
3097640402971548145692349667114318969227988236798317211650887647581456890949971
55418401530487213630171139768049032...(94 digits)...04377473001825917439998365846080751
19141073419134423433532271791072184...(112 digits)...20269710768166130813548607454812401
10239670856890031147835197843264363...(18683 digits)...23258286999621663816504998582744441
827
44083957modified 2024-11-22 08:53:19 created 2024-11-22 08:49:59 id 184627
field value prime_id 124011 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(43326^12041-1)/43325" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (43326^12041-1)/43325 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.26% and helper 0.01% (0.78% proof) (43326^12041-1)/43325 is Fermat and Lucas PRP! (356.5520s+0.0013s) [Elapsed time: 5.95 minutes] modified 2020-07-07 22:30:15 created 2017-11-21 19:01:01 id 169674
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.