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2018-04-06, 17:26   #111
JeppeSN

"Jeppe"
Jan 2016
Denmark

2×89 Posts

Quote:
 Originally Posted by axn Code: (3^2+1^2)/2 (3^4+1^4)/2 (5^8+3^8)/2 (3^16+1^16)/2 (3^32+1^32)/2 (3^64+1^64)/2 (179^128+177^128)/2 (169^256+167^256)/2 (935^512+933^512)/2 (663^1024+661^1024)/2
Submitted as A302387 (not approved yet). /JeppeSN

2018-12-15, 23:24   #112
JeppeSN

"Jeppe"
Jan 2016
Denmark

2·89 Posts

Quote:
 Originally Posted by Batalov Aw well, m=16 was too easy. Even a pair for the good measure: 124^65536+57^65536 143^65536+106^65536
I just discovered these are duplicates at the PRP Top site. If you search for x^(2^16)+y^(2^16), the same two numbers were found by Valeryi Kuryshev in Feb 2011.

/JeppeSN

 2018-12-16, 00:17 #113 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,901 Posts Yes, there are many more; I've seen duplicates in other classes before. (Because there are similarly different ways to write values, e.g. using Phi(), or gcd() ... for primitive parts or Aurifeuillean parts. PRP owners should better have an in-take evaluator and checker. The bracketed form is hard to search for. You can use "x^?+y^?" and then filter, but that's not the first form that comes to mind.
 2018-12-16, 00:35 #114 JeppeSN     "Jeppe" Jan 2016 Denmark 2×89 Posts OK. And still no trace of A291944(17), the smallest PRP of form xGF(17, a, b) = a^131072 + b^131072. /JeppeSN
 2018-12-16, 01:57 #115 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,901 Posts How far did anybody search?
 2022-08-02, 15:30 #116 JeppeSN     "Jeppe" Jan 2016 Denmark 2×89 Posts Kellen Shenton found the PRP 1196^131072 + 595^131072, to appear on PRP Top. As soon as it is verified that 1196 is minimal for this exponent, OEIS will be updated. /JeppeSN

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