3 251 Exponent Status

Great Internet Mersenne Prime Search
GIMPS
Finding World Record Primes Since 1996

PrimeNet Exponent Status

M_n

Status

Details

Composite, with 4 known prime factors. Cofactor is composite.

Factored

Factor	Digits	Bits	Date
1664104461143	13	40.6	old
3456638814270034225163991562199781154565497	43	141.3	2019-01-14 05:03:45
828650800825929189089008897320263379057001769069372383	54	179.1	2019-10-08 14:09:57
9974057717357180877970900136017929397441078565532415870374886351	64	212.6	2021-06-22 14:13:55

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	9201 / 9201
50	44000000	16550 / 16550
55	110000000	14910 / 40830

Estimated T-Level: 51.8 ⓘ

TF below 2^167 is very unlikely to find new factors due to ECM effort.

Status	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified (Factored)	2017-09-21	Oliver Kruse	88FFA64E8A2B64A4	1	0	1	3
Verified (Factored)	2017-10-12	kkmrkkblmbrbk	88FFA64E8A2B64A4	1	1043	1	3
Verified (Factored)	2019-01-15	GunnarLu	5F245C930B7F94E1	2	3072	5	3
Verified (Factored)	2019-01-15	kkmrkkblmbrbk	5F245C930B7F94E1	2	1624	5	3
Verified (Factored)	2019-10-09	mnd9	5F245C930B7F94E1	3	1600	5	3
Verified (Factored)	2020-04-17	Oliver Kruse	5F245C930B7F94E1	3	2415	5	3
Verified	2021-06-22	Yizhe Huang	5F245C930B7F94E1	4	2709	5	3

History

Date	User	Type	Result
2024-05-14	masser	NF-PM1	B1=77000000000, B2=156801561422606100
2021-07-09	ViliamF	NF-PM1	B1=1000000000, B2=191000000000
2021-06-22	Yizhe Huang	C-PRP	M3251/1664104461143/3456638814270034225163991562199781154565497/828650800825929189089008897320263379057001769069372383/9974057717357180877970900136017929397441078565532415870374886351 : 5F245C930B7F94E1 PRP: Verified PRP without proof (small exponent)
2021-06-22	Ryan Propper	F-ECM	Factor: 9974057717357180877970900136017929397441078565532415870374886351 / (ECM curve 1, B1=850000000, B2=15399942768226, Sigma=15727121288461335053)
2020-04-17	Oliver Kruse	C-PRP	M3251/1664104461143/3456638814270034225163991562199781154565497/828650800825929189089008897320263379057001769069372383 : 5F245C930B7F94E1 PRP: Verified PRP without proof (small exponent)
2019-10-09	mnd9	C-PRP	M3251/1664104461143/3456638814270034225163991562199781154565497/828650800825929189089008897320263379057001769069372383 : 5F245C930B7F94E1 PRP: Verified PRP without proof (small exponent)
2019-10-08	Ryan Propper	F-ECM	Factor: 828650800825929189089008897320263379057001769069372383 / (ECM curve 1, B1=110000000)
2019-01-15	kkmrkkblmbrbk	C-PRP	M3251/1664104461143/3456638814270034225163991562199781154565497 : 5F245C930B7F94E1 PRP: Verified PRP without proof (small exponent)
2019-01-15	GunnarLu	C-PRP	M3251/1664104461143/3456638814270034225163991562199781154565497 : 5F245C930B7F94E1 PRP: Verified PRP without proof (small exponent)
2019-01-14	James Hintz	F-ECM	Factor: 3456638814270034225163991562199781154565497 / (ECM curve 2077, B1=11000000, B2=1100000000)
2017-10-12	kkmrkkblmbrbk	C-PRP	M3251/1664104461143 : 88FFA64E8A2B64A4 PRP: Verified PRP without proof (not generated)
2017-09-21	Oliver Kruse	C-PRP	M3251/1664104461143 : 88FFA64E8A2B64A4 PRP: Verified PRP without proof (not generated)
2017-09-21	Oliver Kruse	C-PRP	M3251/1664104461143 : 88FFA64E8A2B64A4 PRP without proof (not generated)