3 343 Exponent Status

PrimeNet Exponent Status

M_n

Details

Composite, with 2 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
21395366139013330348249888032891790630577329313	47	153.9	old
42322984464484074454665873278599117747583616091199	50	164.9	2019-09-20 12:27:17

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	15711 / 40830

Estimated T-Level: 51.9 ⓘ

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

PRP Cofactor

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Factored	No proof (small exponent)	2017-09-21	Oliver Kruse	5F9EFDD250F5052C	1	0	1	3
Factored	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	5F9EFDD250F5052C	1	0	1	3
Factored	No proof (small exponent)	2017-12-07	ATH	5F9EFDD250F5052C	1	1853	1	3
Verified	No proof (small exponent)	2019-09-21	mnd9	88DF67EEF8632327	2	3191	5	3
Verified	No proof (small exponent)	2019-09-22	GAN	88DF67EEF8632327	2	3066	5	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	88DF67EEF8632327	2	1499	5	3

History

Date	User	Type	Result
2025-04-26	masser	NF-PP1	Start=83/41, B1=3100000000, B2=3096900000000
2024-05-20	masser	NF-PM1	B1=77000000000, B2=107407104446211570
2021-07-10	ViliamF	NF-PM1	B1=1000000000, B2=193000000000
2020-04-17	Oliver Kruse	C-PRP	M3343/21395366139013330348249888032891790630577329313/42322984464484074454665873278599117747583616091199 : 88DF67EEF8632327
2019-09-22	GAN	C-PRP	M3343/21395366139013330348249888032891790630577329313/42322984464484074454665873278599117747583616091199 : 88DF67EEF8632327
2019-09-21	mnd9	C-PRP	M3343/21395366139013330348249888032891790630577329313/42322984464484074454665873278599117747583616091199 : 88DF67EEF8632327
2019-09-20	Ryan Propper	F-ECM	Factor: 42322984464484074454665873278599117747583616091199
2017-12-07	ATH	C-PRP	M3343/21395366139013330348249888032891790630577329313 : 5F9EFDD250F5052C
2017-10-02	kkmrkkblmbrbk	C-PRP	M3343/21395366139013330348249888032891790630577329313 : 5F9EFDD250F5052C
2017-09-21	Oliver Kruse	C-PRP	M3343/known_factors : 5F9EFDD250F5052C
2003-02-16	Alex Kruppa	NF	no factor TF: 1-57
2003-01-25	Alex Kruppa	NF	no factor TF: 1-57
2002-12-31	-anonymous-	NF-PM1	B1=4290000000
2002-09-14	-anonymous-	NF-PM1	B1=3221225472, B2=4290000000, E=48
2002-08-03	-anonymous-	NF-PM1	B1=2147483648, B2=4290000000, E=48
2002-06-02	-anonymous-	NF-PM1	B1=1073741824, B2=4290000000
2001-06-09	-anonymous-	NF-PM1	B1=43000000, B2=4290000000
2001-06-09	-anonymous-	NF-PM1	B1=3000000000, B2=4290000000
2001-02-11	-anonymous-	NF-PM1	B1=1000000, B2=100000000
2000-08-17	-anonymous-	NF	no factor TF: 1-56
2000-02-01	-anonymous-	NF	no factor TF: 54-55
1999-12-23	-anonymous-	NF	no factor TF: 53-54
1999-09-22	-anonymous-	NF	no factor TF: 52-53
1998-05-01	Alex Kruppa	NF	no factor TF: 50-51
1998-04-27	Alex Kruppa	NF	no factor TF: 50-51

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