View Single Post
Old 2020-07-14, 17:59   #3
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

2448 Posts
Default

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.
pxp is online now   Reply With Quote