13 417 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
322009	6	18.3	old
2395417513	10	31.2	2008-08-26 19:58:40
3072333110066569270711	22	71.4	2008-08-29 02:24:32
346803621886284269797029562633	30	98.1	2017-05-23 07:13:24

P-1 factors

Date	Factors	B1	B2
2023-12-19	No new factors discovered	100000000000	122154521813133808

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	1576 / 9201

Estimated T-Level: 40.9 ⓘ

TF below 2^131 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	7209DCB9B98C16CA	4	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	7209DCB9B98C16CA	4	0	1	3
Verified	No proof (small exponent)	2017-12-07	ATH	7209DCB9B98C16CA	4	13296	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	D6A88EDE7F83854D	4	1170	5	3
Verified	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	D6A88EDE7F83854D	4	11522	5	3

History

Date	User	Type	Result
2025-02-26	masser	NF-PP1	Start=177/41, B1=430000000, B2=429570000000
2025-02-12	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-27	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M13417/2395417513/3072333110066569270711/322009/346803621886284269797029562633 : D6A88EDE7F83854D
2023-12-19	-anonymous-	F-PM1	Factor: 346803621886284269797029562633 / B1=100000000000, B2=122154521813133810
2023-05-19	JacobZ	NF-PM1	B1=8200000000, B2=35024272926292650
2022-02-05	Joss	NF-PM1	B1=1000000, B2=3910366209750
2020-04-17	Oliver Kruse	C-PRP	M13417/322009/2395417513/3072333110066569270711/346803621886284269797029562633 : D6A88EDE7F83854D
2017-12-07	ATH	C-PRP	M13417/322009/2395417513/3072333110066569270711/346803621886284269797029562633 : 7209DCB9B98C16CA
2017-10-02	kkmrkkblmbrbk	C-PRP	M13417/322009/2395417513/3072333110066569270711/346803621886284269797029562633 : 7209DCB9B98C16CA
2017-09-21	Oliver Kruse	C-PRP	M13417/322009/2395417513/3072333110066569270711/346803621886284269797029562633 : 7209DCB9B98C16CA
2017-05-23	kkmrkkblmbrbk	F-ECM	Factor: 346803621886284269797029562633
2008-08-29	-anonymous-	F-ECM	Factor: 3072333110066569270711
2008-08-26	-anonymous-	F	Factor: 2395417513