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

[pxp]

Originally Posted by japelprime

I do not want to do uncontrolled Sieve range or solo work out of the blue here. To messy. Any gabs to close maybe if that will help ?

All of the gaps in my table are just as you see them. That is from 150000 decimal digits to 300000 decimal digits and greater than 305000 decimal digits, with the exception of the four from 386434 to 386642 decimal digits. That is, they are organized by decimal-digit size. I think Norbert Schneider still uses an (x,y) search approach to his prime finds but just limits his ranges to be sufficiently large. He has not shared which ranges he has actually tried. I don't know how Gabor Levai found his very large primes but I suspect that his approach is closer to my own, which is to organize Leyland (x,y) pairs by digit-size and sieve them that way. For example, the (x,y) pairs of Leyland numbers with exactly one million digits are, in order of increasing size, tabled here.

[NorbSchneider]

Another new PRP:
38442^38531+38531^38442, 176658 digits.

[japelprime]

PXP your data are good document to hold things in perspective. Thanks
Here we have a prime chart as I find here in the latest data replay from PXP. PXP It is upgrade what I see you have been doing earlier. Easier to estimate the Sieve range that have been done until now. I am not sure if I have all data,

[pxp]

The chart looks good. Why are some of the points orange?

[pxp]

Originally Posted by pxp

Why are some of the points orange?

Never mind. My reproduction here shows that they are likely the points (currently 37) discovered in 2022.

[japelprime]

Originally Posted by pxp

Never mind. My reproduction here shows that they are likely the points (currently 37) discovered in 2022.

Yes Correct.

[lghu]

A new PRP (currently pfgw64 -f only):
105098^61113+61113^105098
503014 digit, index: 6153473043, discoverer Miklos Levai

[lghu]

I found another PRP:
101863^84922+84922^101863 [502085 digit] index: 6132803185

[lghu]

The next PRP index: 6136565930.
pxp: This is enough for you?

[NorbSchneider]

lghu: I like to know what is the new leyland PRP. For me is PRP index no help. Are you from Hungary, can you speak hungarian? I am from Hungary and also search Leyland primes.

[pxp]

Originally Posted by lghu

The next PRP index: 6136565930.
pxp: This is enough for you?

No. Back in March I created a dictionary of Leyland (x,y) pairs from (999999,10) to (1000999,10), sorted by magnitude and preceded by its Leyland-number index (21588818851 to 21628375832). So I can look up the (x,y) pair if the index is within that bound. But I have no similar dictionary for your index, which corresponds to ~502250 decimal digits.