Leyland Primes (x^y+y^x primes)

[lghu]

Next PRP: 101070^88579+88579^101070 [500027 digit]


An error message was also received:

Error occuring in PFGW at Fri Jan 14 17:43:16 2022
Expr = ((101550^101521)+(101521^101550))
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 161146/1688920 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a1

trial factoring to 192534481
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 161146/1688920 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a1
((101550^101521)+(101521^101550)) is composite: RES64: [70F0EEC7C1585A79]

Is there something to do or not?

[paulunderwood]

Originally Posted by lghu

Next PRP: 101070^88579+88579^101070 [500027 digit]

Congrats!

PFGW will automatically rerun the test with -a1
((101550^101521)+(101521^101550)) is composite: RES64: [70F0EEC7C1585A79]

Is there something to do or not?

No. PFGW ran successfully with a bigger FFT size using -a1

[lghu]

A few days later (same machine):

Error occuring in PFGW at Mon Jan 17 03:15:02 2022
Expr = ((101550^101189)+(101189^101550))
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 533346/1688440 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a1
-----------------------------------------------------------------------
Error occuring in PFGW at Mon Jan 17 03:21:09 2022
Expr = ((101550^101189)+(101189^101550))
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 27591/1688440 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a2
-----------------------------------------------------------------------
Error occuring in PFGW at Mon Jan 17 03:29:18 2022
Expr = ((101550^101189)+(101189^101550))
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 33640/1688440 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a3
-----------------------------------------------------------------------
Error occuring in PFGW at Mon Jan 17 03:32:46 2022
Expr = ((101550^101189)+(101189^101550))
Detected in gw_test_illegal_sumout() in prp_using_gwnum
Iteration: 13406/1688440 ERROR: ILLEGAL SUMOUT
PFGW will automatically rerun the test with -a4

And:

((101550^101189)+(101189^101550)) is composite: RES64: [13DA6493101F6E90]

Could it be a hardware failure?

[rogue]

Originally Posted by lghu

((101550^101189)+(101189^101550)) is composite: RES64: [13DA6493101F6E90]

Could it be a hardware failure?

If this happened consistently, then maybe, but everyone once in a while, probably not.

[lghu]

Currently biggest Leyland PRP: 107890^49423+49423^107890 [506429 digit].
The discoverer was my brother Miklos Levai.

[pxp]

Originally Posted by lghu

Currently biggest Leyland PRP: 107890^49423+49423^107890 [506429 digit].
The discoverer was my brother Miklos Levai.

Congratulations to Miklos. By the way, my list of all known Leyland primes tries hard to stay up-to-date but I will calculate an associated Leyland number index (the prime's position in OEIS sequence A076980) before I post a new entry. For these large numbers this takes me about 24 hours. I recently attempted to interest the Mathematica community in speeding up the program that I wrote to do this but have had no such improvement.

[pxp]

I have now finished testing the Leyland numbers in the interval from L(302999,10) to L(303999,10) and have found therein 14 PRPs. Next interval is L(303999,10) - L(304999,10).

[lghu]

A new Leyland PRP: 101761^82168+82168^101761, 500126 digit.
Index: 6089270621 (I hope the right value.)

[NorbSchneider]

Another new PRP:
414^62093+62093^414, 162498 digits.

[pxp]

To Norbert & Ighu: Have either of you been getting email confirmations for your PRPtop submissions? I had a time in mid- to late-December when I wasn't getting them and then, again, starting in mid-February. In fact, I've had no confirmation since then even though they were all received.

[lghu]

I didn’t get it from March 2022, I got it before.