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

[XYYXF]

Originally Posted by firejuggler

I was pretty sure It was already reserved. If no one volonteer before I come back from my trip ( mid december) ten i'll do it.

It seems the range is still available :)

[NorbSchneider]

I reached x=42,000 and found one new PRP:
322^41507+41507^322, 104094 digits.

I reached x=36,000 and found two new PRPs:
302^35829+35829^302, 88857 digits,
214^35917+35917^214, 83702 digits.

[NorbSchneider]

I reached x=38,100 and found three new PRPs:
265^37614+37614^265, 91148 digits,
243^37738+37738^243, 90029 digits,
249^38030+38030^249, 91128 digits.

[NorbSchneider]

I reserve the interval:
50,001<=x<=500,000, 19<=y<=25.

[XYYXF]

That's quite a big interval. Good luck with it.

Note the changed URL of the page: http://www.primefan.ru/xyyxf/primes.html#0

[NorbSchneider]

The interval 20,001<=x<=40,000, 201<=y<=400 is done, no new PRPs.
The last was 249^38030+38030^249, 91128 digits.

In the interval 40,001<=x<=50,000, 19<=y<=400 reached I x=48,695 and found two new PRPs:
286^45405+45405^286, 111532 digits.
317^48694+48694^317, 121787 digits.

In the interval 50,001<=x<=500,000, 19<=y<=25 reached I x=161,000, no new PRPs.

[NorbSchneider]

The interval 40,001<=x<=50,000, 19<=y<=400 is done, no new PRPs.

In the interval 50,001<=x<=500,000, 19<=y<=25 reached I x=186,000, no new PRPs.

I search also in the interval 12,501<=x<=13,000, 2001<=y<=x-1.
Please reserve this interval for me.
I read firejuggler searched the interval x=12501->15000, y=2501->3000.

I reached x=12,547 and found two new PRPs:
4114^12547+12547^4114, 45349 digits,
4354^12547+12547^4354, 45658 digits.

I found 3 PRPs on prptop, discovered by Hans Havermann.
13350^9739+9739^13350, 53247 digits,
14394^4993+4993^14394, 53235 digits,
13739^4600+4600^13739, 50323 digits.

[XYYXF]

Originally Posted by NorbSchneider

I search also in the interval 12,501<=x<=13,000, 2001<=y<=x-1.
Please reserve this interval for me.

Thank you Norbert. Please note that the lower bound for y is 3001 here, not 2001.

[pxp]

Originally Posted by NorbSchneider

I found 3 PRPs on prptop, discovered by Hans Havermann.

Thank you for noticing. When I first encountered Leyland primes last April, I got to wondering how many of the smallest ones were consecutive. I guessed at least 954 and it was my intention to verify that by making sure there were no additional primes in that range. The computation is ongoing and has several months to go. More recently, I got bored with the work and decided to divert a couple of my cores to check some smallish gaps between larger Leyland primes. This is how the 3 PRPs were discovered. Because I'm not limiting myself to XYYXF's reservation regime, I realize that I may be stepping on some toes. I apologize for that but it is unavoidable.

[NorbSchneider]

I reached x=12,650 and found 5 new PRPs:
9992^12549+12549^9992, 50192 digits,
11835^12584+12584^11835, 51257 digits,
8482^12591+12591^8482, 49464 digits,
9035^12622+12622^9035, 49932 digits,
3900^12643+12643^3900, 45402 digits.

[NorbSchneider]

I reached x=12,700 and found 5 new PRPs:
9737^12654+12654^9737, 50470 digits,
8530^12677+12677^8530, 49833 digits,
5755^12682+12682^5755, 47685 digits,
6213^12682+12682^6213, 48107 digits,
11008^12697+12697^11008, 51318 digits.