mersenneforum.org Reservations fop x^y+y^x
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 2020-07-14, 12:48 #1 rogue     "Mark" Apr 2003 Between here and the 22×3×487 Posts Reservations fop x^y+y^x This thread is to capture reservations and completed ranges per this page. There is another search for primes of this form, but that search is by decimal length not by range of x and y. Those reservations are not managed by this thread. At this time all y have been tested for all x <= 13000. Note that y < x as we want x^y > y^x.
 2020-07-14, 12:51 #2 rogue     "Mark" Apr 2003 Between here and the 10110110101002 Posts I will reserve all y for 13001 <= x <= 15000. I will also double-check from x=12501 to x = 13000. I will do all I can to avoid stepping on the toes of the other search for primes of this form less than 100,000 decimal digits. If anything I will be double-checking their work. They will likely complete their search before I start testing the range they are working on. Last fiddled with by rogue on 2020-07-14 at 12:56
 2020-07-14, 17:59 #3 pxp     Sep 2010 Weston, Ontario 2×3×52 Posts The largest x^y+y^x occurs for y=x which for a given x-range occurs for the largest x in that range. Thus, the largest Leyland number up to x=13000 is 2*13000^13000, which has 53482 decimal digits. Here is a table of Leyland number decimal digits for largest x from 13000 to 30000 at intervals of 1000: 13000 53482 14000 58047 15000 62642 16000 67267 17000 71918 18000 76596 19000 81297 20000 86021 21000 90767 22000 95534 23000 100321 24000 105126 25000 109949 26000 114790 27000 119648 28000 124521 29000 129410 30000 134314 This will give you an idea of where the overlap between the two systems lies. Having checked all Leyland numbers smaller than (currently) 84734 decimal digits implies (barring errors) that I have checked all x smaller than 19728. That allows me to suggest that this table of x, y values (based on Andrey Kulsha's ordering) is complete. Of course it would be nice to have verification.
2020-07-14, 18:41   #4
rogue

"Mark"
Apr 2003
Between here and the

22·3·487 Posts

Quote:
 Originally Posted by pxp The largest x^y+y^x occurs for y=x which for a given x-range occurs for the largest x in that range. Thus, the largest Leyland number up to x=13000 is 2*13000^13000, which has 53482 decimal digits. Here is a table of Leyland number decimal digits for largest x from 13000 to 30000 at intervals of 1000: 13000 53482 14000 58047 15000 62642 16000 67267 17000 71918 18000 76596 19000 81297 20000 86021 21000 90767 22000 95534 23000 100321 24000 105126 25000 109949 26000 114790 27000 119648 28000 124521 29000 129410 30000 134314 This will give you an idea of where the overlap between the two systems lies. Having checked all Leyland numbers smaller than (currently) 84734 decimal digits implies (barring errors) that I have checked all x smaller than 19728. That allows me to suggest that this table of x, y values (based on Andrey Kulsha's ordering) is complete. Of course it would be nice to have verification.
Thanks. In the worst case scenario I will be double-checking your work, which shouldn't hurt anyone. I don't expect that to take too long after sieving.

If double-checking reveals no missed primes, then I might forego double-checking for larger x.

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