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Old 2022-06-06, 15:40   #3
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Dec 2003

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Yes, this is the initial test + double check on M3936727 = 23936727-1
Status			Date		User		Residue			Shift
Verified (Factored)	1998-01-26	Soh Kok Hong	7D98BB85E98906AA	0
Verified (Factored)	1999-12-01	Rob Simons	7D98BB85E98906AA	2768285
Then the 1st factor was found and we check if the remaining cofactor M3936727 / 1416543718452177641 is prime or composite. This is not part of the main GIMPS project to find Mersenne Primes, but a side project to find as many factors as possible and check if we found them all for each exponent.

The first 2 PRP Cofactor tests was in 2017 before PRP Certification / Proof and I think back then when PRP CF was just implemented only "Type 1" test was available.
Then 2nd factor was found and now we test the remaining cofactor: M3936727 / (1416543718452177641*2542680988412771022521) so it gives a different residue with 2 factors, and this time with a "Type 5" test, which will give a different residue from Type 1 even if the number of factors was the same.
The advantage of Type 5 is if a 3rd factor is found and Type 5 is run on the remaining cofactor, it will give the same residue as with 2 factors, so only 1 test is needed (and no PRP Certification needed). This advantaged with Type 5 is not that important now that we have PRP Certifications.

PRP Cofactor	
Status			Date		User		Residue		Number of known factors	Shift	Type	Base
Verified (Factored)	2022-06-03	Loic		70D58841F6D82E77	2		3198615	5	3
Verified (Factored)	2017-12-30	Oliver Kruse	81659F6303C264C5	1		1531080	1	3
Verified (Factored)	2017-09-20	kkmrkkblmbrbk	81659F6303C264C5	1		0	1	3
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