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Old 2020-08-07, 11:25   #397
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I will likely do a search for Leyland primes between L(49878,755) and L(149999,10), so as to establish a new beachhead for my advance.
I have added indicators for intervals #19-#21 to my list. I have also decided that the above mentioned "beachhead" is far too ambitious. My intended beachhead is now interval #21. I am still in the process of verifying my new list of Leyland numbers which runs from L(102999,10) to L(149999,10), 337553864 terms. A worthwhile guide is that for d > 11, L(d-1,10) is (likely) the smallest (base ten) d-digit term. The sorted-by-magnitude list will allow me to directly look up the Leyland number index of any (x,y) term in that range. It will also, of course, provide the seed (x,y) pairs needed to generate the ABC files for my intervals.
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Old 2020-08-07, 18:59   #398
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Another new PRP:
1678^28479+28479^1678, 91839 digits.
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Old 2020-08-14, 09:40   #399
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That makes L(91382,9) #1660.
I have examined all Leyland numbers in the six gaps between L(91382,9) <87201>, #1660, and L(35829,302) <88857> and found 27 new primes. That makes L(35829,302) #1693.
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Old 2020-08-20, 11:50   #400
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That makes L(35829,302) #1693.
I have examined all Leyland numbers in the two gaps between L(35829,302) <88857>, #1693, and L(37738,243) <90029> and found 20 new primes. That makes L(37738,243) #1715.
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Old 2020-08-21, 21:05   #401
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A worthwhile guide is that for d > 11, L(d-1,10) is (likely) the smallest (base ten) d-digit term.
I began to wonder if any of these L(x,10) is prime. I'm doing a run on a list that I didn't sieve particularly deeply and I can say that for x < 300000 the answer is none. Perhaps this had already been determined. Of the prime L(x,y) that have x > 50000, I count 13 (current) solutions: (57285,2), (58046,9), (63880,3), (78296,3), (91382,9), (99069,2), (104824,5), (125330,3), (222748,3), (234178,9), (255426,11), (314738,9), (328574,15). All small y, which makes me wonder how far the discoverers allowed x to go (and for which y).

I've put a compilation of small-y solutions (y <= 1000) here.
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Old 2020-08-26, 05:06   #402
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That makes L(37738,243) #1715.
I have examined all Leyland numbers in the two gaps between L(37738,243) <90029>, #1715, and L(38030,249) <91128> and found 17 new primes. That makes L(38030,249) #1734 and advances the index to L(37614,265), #1735.
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Old 2020-09-06, 09:21   #403
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My intended beachhead is now interval #21.
I decided to take my sieving of interval #21 to 1e10 and that still has a couple of days to go. In the meantime I am pfgw-ing recently assigned (and already sieved) interval #28 [L(148999,10) - L(149999,10)] and have now my first hit therein:

33845^26604+26604^33845 is 3-PRP!

I'm not sure factordb.com will PRP this for me. I noticed that Norbert's PRPTop submissions for a couple of his larger Leyland primes has a list of prime-PRPs from prime 2 to 11. Which brings me to ask why pfgw default reports only 3-PRPs. How does one get it to do other primes? Is it even necessary?
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Old 2020-09-06, 14:07   #404
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I decided to take my sieving of interval #21 to 1e10 and that still has a couple of days to go. In the meantime I am pfgw-ing recently assigned (and already sieved) interval #28 [L(148999,10) - L(149999,10)] and have now my first hit therein:

33845^26604+26604^33845 is 3-PRP!

I'm not sure factordb.com will PRP this for me. I noticed that Norbert's PRPTop submissions for a couple of his larger Leyland primes has a list of prime-PRPs from prime 2 to 11. Which brings me to ask why pfgw default reports only 3-PRPs. How does one get it to do other primes? Is it even necessary?
Use -b to choose a different base for the PRP test.
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