Leyland Primes (x^y+y^x primes) - Page 44

lghu · 2021-09-09, 08:18

I found a Leyland PRP with more than 500,000 digits, details later...

lghu · 2021-09-11, 12:38

pfgw64: ((100263^98600)+(98600^100263)) is 3-PRP! (7167.1435s+0.0099s)

ecpp-dj -bpsw: ((100263**98600)+(98600**100263)) PROBABLE PRIME (135355 sec)

Gabor Levai

paulunderwood · 2021-09-11, 12:43

Quote:

Originally Posted by lghu

pfgw64: ((100263^98600)+(98600^100263)) is 3-PRP! (7167.1435s+0.0099s)

ecpp-dj -bpsw: ((100263**98600)+(98600**100263)) PROBABLE PRIME (135355 sec)

Gabor Levai

Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker.

Congrats for such a huge find.

pxp · 2021-09-12, 09:33

100263^98600+98600^100263,500702

If you haven't already done so, you should submit this to PRPTop, here.

lghu · 2021-09-13, 08:39

Quote:

Originally Posted by paulunderwood

Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker.

Congrats for such a huge find.

Thanks.
((100263^98600)+(98600^100263)) is Fermat and Lucas PRP! (37359.5544s+0.0101s)

NorbSchneider · 2021-11-05, 10:48

Another new PRP:
35820^35899+35899^35820, 163489 digits.

pxp · 2021-11-06, 02:51

I have now finished testing the Leyland numbers in the interval from L(300999,10) to L(301999,10) and have found therein 12 PRPs. Next interval is L(301999,10) - L(302999,10).

lghu · 2021-11-09, 12:19

A prime number: 100207, a square number: 99856 (=316^2), a PRP: 100207^99856+99856^100207.

pxp · 2021-12-21, 12:09

In order to occupy a handful of old spare cores, I've been sieving a small number of my "LLPH" [greater than Yusuf AttarBashi's L(81650,54369), less than L(390000,10)] Leyland numbers. The by-digit-length sieved files average 300-or-so candidates, plus-or-minus 40. I was curious how fast the candidates would PFGW-resolve on a recently-acquired 2020 iMac, so I took the file for digit-length 390000 and ran it.

I guessed that I had maybe a 1% chance of finding a PRP, but I got lucky: L(95196,12497).

lghu · 2021-12-21, 13:34

I found a new PRP: 101311^90816+90816^101311 [502317 digit].

pxp · 2022-01-11, 01:07

I have now finished testing the Leyland numbers in the interval from L(301999,10) to L(302999,10) and have found therein 10 PRPs. Next interval is L(302999,10) - L(303999,10).

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2021-09-09, 08:18	#474
lghu Nov 2019 15₈ Posts	I found a Leyland PRP with more than 500,000 digits, details later...

2021-09-11, 12:38	#475
lghu Nov 2019 13 Posts	pfgw64: ((100263^98600)+(98600^100263)) is 3-PRP! (7167.1435s+0.0099s) ecpp-dj -bpsw: ((10026398600)+(98600100263)) PROBABLE PRIME (135355 sec) Gabor Levai

2021-09-12, 09:33	#477
pxp Sep 2010 Weston, Ontario 2×107 Posts	100263^98600+98600^100263,500702 If you haven't already done so, you should submit this to PRPTop, here.

2021-11-05, 10:48	#479
NorbSchneider "Norbert" Jul 2014 Budapest 2⁴·7 Posts	Another new PRP: 35820^35899+35899^35820, 163489 digits.

2021-11-06, 02:51	#480
pxp Sep 2010 Weston, Ontario 2×107 Posts	I have now finished testing the Leyland numbers in the interval from L(300999,10) to L(301999,10) and have found therein 12 PRPs. Next interval is L(301999,10) - L(302999,10).

2021-11-09, 12:19	#481
lghu Nov 2019 13 Posts	A prime number: 100207, a square number: 99856 (=316^2), a PRP: 100207^99856+99856^100207.

2021-12-21, 12:09	#482
pxp Sep 2010 Weston, Ontario 214₁₀ Posts	In order to occupy a handful of old spare cores, I've been sieving a small number of my "LLPH" [greater than Yusuf AttarBashi's L(81650,54369), less than L(390000,10)] Leyland numbers. The by-digit-length sieved files average 300-or-so candidates, plus-or-minus 40. I was curious how fast the candidates would PFGW-resolve on a recently-acquired 2020 iMac, so I took the file for digit-length 390000 and ran it. I guessed that I had maybe a 1% chance of finding a PRP, but I got lucky: L(95196,12497).

2021-12-21, 13:34	#483
lghu Nov 2019 13 Posts	I found a new PRP: 101311^90816+90816^101311 [502317 digit].

2022-01-11, 01:07	#484
pxp Sep 2010 Weston, Ontario 2×107 Posts	I have now finished testing the Leyland numbers in the interval from L(301999,10) to L(302999,10) and have found therein 10 PRPs. Next interval is L(302999,10) - L(303999,10).