Leyland Primes: ECPP proofs

[xilman]

Uploaded L(4153,2154)

Reserving (3892,765)

[frmky]

(3423,3070) is done, and FactorDB is verifying.
I'll reserve (3712,1407).

[pxp]

Originally Posted by frmky

Are certificates for (2930,2739) and (3265,1234) available anywhere? They are not in FactorDB, a Google search came up empty, and they aren't listed on François Morain's site.

I've just rediscovered on old document of mine wherein I had noted (at the time) 25 proven-prime listings in Kulsha's database that were still PRP in factordb. Going through them, I note that now all but 4 of them are P in factordb. These 4 are:

298 5769007 10073 (2930,2739)
299 5789897 10094 (3265,1234)
621 28333594 25050 (6753,5122)
715 38951950 30008 (8656,2929)

In my Leyland-prime masterlist, I will change the current P to a K to indicate that.

[frmky]

I just uploaded a certificate for (6753,5122). I might rerun the first two soon since no certificate seems to be available.

[xilman]

Originally Posted by xilman

Uploaded L(4153,2154)

Reserving (3892,765)

Uploaded (3892,765)

Thinking whether to do another one or whether to return to factoring.

[frmky]

(57285,2) is done. (78296,3) is in progress.

[frmky]

(3213,2942) is done.

[storm5510]

Originally Posted by xilman

Taking 4153^2154 + 2154^4153

4153^2154+2154^4153 is 3-PRP! (2.0381s+0.0021s)

The above only took a few seconds. You must be running it in a different way?

[paulunderwood]

Originally Posted by storm5510

The above only took a few seconds. You must be running it in a different way?

This is prime hunting 101. The number 91 is 3-PRP yet factors into 7*13. To be 100% sure of primality we need to follow a method that actually proves the number prime -- in this case ECPP is used for xilman's number.

[storm5510]

Originally Posted by paulunderwood

This is prime hunting 101. The number 91 is 3-PRP yet factors into 7*13. To be 100% sure of primality we need to follow a method that actually proves the number prime -- in this case ECPP is used for xilman's number.

Very well.

Above, someone mentions (3892,765). 3892^765+765^3892, if I understand the notation correctly. This must be the last value in a range from something lower. I understand how to use pfgw, but this expression of a single sequence throws me.

[paulunderwood]

Originally Posted by storm5510

Very well.

Above, someone mentions (3892,765). 3892^765+765^3892, if I understand the notation correctly. This must be the last value in a range from something lower. I understand how to use pfgw, but this expression of a single sequence throws me.

You understood correctly: (3892,765) is shorthand notation herein for 3892^765+765^3892.