3 853 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 7 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
3390641	7	21.7	old
734002418209	12	39.4	old
435268273460898401	18	58.6	old
4123914511939938969937	22	71.8	old
2100656437769064573899772266936926591	37	120.7	old
257056372314429393905874808530805991327	39	127.6	old
7740376302584257292322119054163431736983551	43	142.5	2009-07-04 21:30:27

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	16584 / 40830

Estimated T-Level: 52.0 ⓘ

TF below 2^168 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	808451E78228A4D9	7	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	808451E78228A4D9	7	0	1	3
Verified	No proof (small exponent)	2017-12-07	ATH	808451E78228A4D9	7	814	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	70F164B018A11E05	7	465	5	3
Verified	No proof (small exponent)	2024-02-03	Wentao Huang	70F164B018A11E05	7	737	5	3

History

Date	User	Type	Result
2025-05-06	masser	NF-PP1	Start=162/71, B1=2600000000, B2=2597400000000
2024-07-09	masser	NF-PM1	B1=77000000000, B2=92033336835039600
2024-02-03	Wentao Huang	C-PRP	M3853/3390641/734002418209/435268273460898401/4123914511939938969937/2100656437769064573899772266936926591/257056372314429393905874808530805991327/7740376302584257292322119054163431736983551 : 70F164B018A11E05
2021-09-09	Jinyuan Wang	NF-PM1	B1=1300000000, B2=13000000000
2020-04-17	Oliver Kruse	C-PRP	M3853/3390641/734002418209/435268273460898401/4123914511939938969937/2100656437769064573899772266936926591/257056372314429393905874808530805991327/7740376302584257292322119054163431736983551 : 70F164B018A11E05
2017-12-07	ATH	C-PRP	M3853/3390641/734002418209/435268273460898401/4123914511939938969937/2100656437769064573899772266936926591/257056372314429393905874808530805991327/7740376302584257292322119054163431736983551 : 808451E78228A4D9
2017-10-02	kkmrkkblmbrbk	C-PRP	M3853/3390641/734002418209/435268273460898401/4123914511939938969937/2100656437769064573899772266936926591/257056372314429393905874808530805991327/7740376302584257292322119054163431736983551 : 808451E78228A4D9
2017-09-21	Oliver Kruse	C-PRP	M3853/known_factors : 808451E78228A4D9
2009-07-04	unconnected	F-ECM	Factor: 7740376302584257292322119054163431736983551
2005-03-20	-anonymous-	F-PM1	Factor: 435268273460898401
2005-03-20	-anonymous-	F-PM1	Factor: 4123914511939938969937