20180325, 20:46  #89 
"Jeppe"
Jan 2016
Denmark
2·7·13 Posts 
I found one for 2^14 and now have:
Code:
(3^(2^0)+1^(2^0))/2 (3^(2^1)+1^(2^1))/2 (3^(2^2)+1^(2^2))/2 (5^(2^3)+3^(2^3))/2 (3^(2^4)+1^(2^4))/2 (3^(2^5)+1^(2^5))/2 (3^(2^6)+1^(2^6))/2 (49^(2^7)+9^(2^7))/2 (7^(2^8)+3^(2^8))/2 (35^(2^9)+9^(2^9))/2 (67^(2^10)+57^(2^10))/2 (49^(2^11)+75^(2^11))/2 (157^(2^12)+83^(2^12))/2 (107^(2^13)+69^(2^13))/2 (71^(2^14)+1^(2^14))/2 /JeppeSN 
20180325, 21:17  #90 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
5·1,997 Posts 
Yes, why not.
Any sequence is a sequence. Most of the text can be reused from the previous sequence, and use this sister sequence for the upper boundary https://oeis.org/A275530 
20180326, 09:15  #91  
"Jeppe"
Jan 2016
Denmark
2×7×13 Posts 
Quote:


20180326, 09:44  #92 
"Jeppe"
Jan 2016
Denmark
182_{10} Posts 
We can also restrict ourselves to consecutive odd bases:
\[\frac{a^{2^n}+(a2)^{2^n}}{2}\] Can also be parametrized in other ways, such as the \(k\) in: \[\frac{(2k+1)^{2^n}+(2k1)^{2^n}}{2}\] OEIS does not seem to have it either (searching for a, or for a2, or for 2k=a1, or for k). /JeppeSN 
20180326, 11:02  #93  
Jun 2003
3^{4}·67 Posts 
Quote:
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 

20180326, 13:23  #94 
Jun 2003
1533_{16} Posts 
So, I sieved n=17 for 0 < b < a <= 2048 till 2^53. Not sure what range or what depth Serge has sieved on this n, but it looks "sieved enough". This could be used to divide up PRP work.
The logic doesn't exactly correspond to gfn/cyclo sieves, so a cuda sieve will have to be built from scratch, more or less; I have to think about it a bit. 
20180326, 16:26  #95  
Feb 2017
Nowhere
2^{2}·1,523 Posts 
Quote:
a^(2^m) + b^(2^m), [or (a^(2^m) + b^(2^m))/2, if a and b are both odd] is a (pseudo)prime in a reasonable length of time. 

20180326, 21:28  #96 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
5·1,997 Posts 
axn's sieve is easily modified for oddodd pairs. In fact nearly nothing needs to be changed (only the intake parity filters, if they are there; they were in mine, just drop them).

20180327, 03:02  #97 
Jun 2003
5427_{10} Posts 
No. The hash matching also needs to change (it currently puts even indexed residues in the hash and uses oddindexed residues to probe the hash).

20180329, 07:23  #98 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10011100000001_{2} Posts 
I am researching a very weird anomaly.
From https://oeis.org/A275530 inquiring minds can find out that a(15) > 10,000. Or in other words, there are no small prps of the GFN' form (a^32768+1)/2. Now, from what I checked with PFGW, a(15) appears to be either > 160,000 (or even >200,000, which is unreasonably high), or there is a bug in libgwnum. I checked with pfgw, llr, p95 but the speed and results are similar (and the underlying lib is the same). All programs chose the special FFT of size 32K. Changing FFT size to a larger one doesn't help to find a PRP yet. Very strange. 
20180329, 08:25  #99  
Jun 2003
3^{4}×67 Posts 
Quote:


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