6 781 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

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

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
108497	6	16.7	old
2091592872431	13	40.9	old
4441550321163963199	19	61.9	old
1321269609013837903207351	25	80.1	old

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	2436 / 16550

Estimated T-Level: 45.7 ⓘ

TF below 2^147 is very unlikely to find new factors due to ECM effort.

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified	No proof (small exponent)	2017-09-21	Oliver Kruse	AC07749F75D4E8D8	4	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	AC07749F75D4E8D8	4	0	1	3
Verified	No proof (small exponent)	2017-12-07	ATH	AC07749F75D4E8D8	4	1641	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	1C9095ECD8AAC60A	4	356	5	3
Verified	No proof (small exponent)	2024-02-03	Wentao Huang	1C9095ECD8AAC60A	4	2500	5	3

History

Date	User	Type	Result
2025-03-22	masser	NF-PP1	Start=105/19, B1=1000000000, B2=999000000000
2025-03-14	masser	NF-PP1	Start=6/5, B1=1000000000, B2=999000000000
2025-03-05	masser	NF-PP1	Start=2/7, B1=1000000000, B2=999000000000
2024-02-03	Wentao Huang	C-PRP	M6781/108497/2091592872431/4441550321163963199/1321269609013837903207351 : 1C9095ECD8AAC60A
2023-08-14	-anonymous-	NF-PM1	B1=36000000000, B2=144600212653396500
2021-12-18	Oliver Kruse	NF-PM1	B1=1000000000, B2=1080854750315340
2020-04-17	Oliver Kruse	C-PRP	M6781/108497/2091592872431/4441550321163963199/1321269609013837903207351 : 1C9095ECD8AAC60A
2017-12-07	ATH	C-PRP	M6781/108497/2091592872431/4441550321163963199/1321269609013837903207351 : AC07749F75D4E8D8
2017-10-02	kkmrkkblmbrbk	C-PRP	M6781/108497/2091592872431/4441550321163963199/1321269609013837903207351 : AC07749F75D4E8D8
2017-09-21	Oliver Kruse	C-PRP	M6781/known_factors : AC07749F75D4E8D8
2009-10-25	Carsten Kossendey	F	Factor: 226931551880146207