20180316, 20:18  #34  
Sep 2002
Database er0rr
D6C_{16} Posts 
Quote:
Code:
time ./pfgw64 k f0 od q"260^32768+179^32768"  ../../coding/gwnum/hybrid 
Testing (x + 2)^(n + 1) == 7 (mod n, x^2  x + 1)...
Likely prime!
real 3m34.502s
user 5m52.580s
sys 1m13.776s


20180316, 20:28  #35 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
m=0, 2^1 + 1^1
m=1, 2^2 + 1^2 m=2, 2^4 + 1^4 m=3, 2^8 + 1^8 m=4, 2^16 + 1^16 m=5, 9^32 + 8^32 m=6, 11^64 + 8^64 m=7, 27^128 + 20^128 m=8, 14^256 + 5^256 m=9, 13^512 + 2^512 m=10, 47^1024 + 26^1024 m=11, 22^2048 + 3^2048 m=12, 53^4096 + 2^4096 m=13, 72^8192 + 43^8192 Aka (72^2)^4096+(43^2)^4096 (53^2)^2048+(2^2)^2048 (22^2)^1024+(3^2)^1024 (47^2)^512+(26^2)^512 (13^2)^256+(2^2)^256 (14^2)^128+(5^2)^128 (27^2)^64+(20^2)^64 (11^2)^32+(8^2)^32 (9^2)^16+(8^2)^16 (2^2)^8+(1^2)^8 (2^2)^4+(1^2)^4 (2^2)^2+(1^2)^2 (2^2)^1+(1^2)^1 Minimal next level= minimal square based current level. Aka Serges previous result has a>14 or b>10 or both for the next level. Last fiddled with by science_man_88 on 20180316 at 21:05 
20180316, 23:00  #36 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,041 Posts 

20180317, 00:20  #37 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 

20180317, 01:06  #38  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,041 Posts 
Quote:
And under a<=600 there are ~4 times more pairs than under a<=300. So what, just keep sieving and testing! What seems to be the problem? It is excellent that the number of tries goes quadratic  you go almost flat in size (and in test runtime); and one likely need to test γ*2^m pairs, i.e. ~30,000 to 40,000. Just keep sieving and testing! 

20180317, 01:59  #39  
"Forget I exist"
Jul 2009
Dumbassville
20B1_{16} Posts 
Quote:


20180317, 02:39  #40 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,041 Posts 
Aw well, m=16 was too easy. Even a pair for the good measure:
124^65536+57^65536 143^65536+106^65536 
20180317, 02:58  #41 
Jun 2003
2·13·181 Posts 

20180317, 03:08  #42  
Sep 2002
Database er0rr
2^{2}·859 Posts 
Quote:
Code:
time ./pfgw64 k f0 od q"124^65536+57^65536"  ../../coding/gwnum/hybrid  Testing (x + 1)^(n + 1) == 2 + 3 (mod n, x^2  3*x + 1)... Likely prime! real 8m40.139s user 15m28.568s sys 1m48.060s Code:
time ./pfgw64 k f0 od q"143^65536+106^65536"  ../../coding/gwnum/hybrid  Testing (x + 2)^(n + 1) == 7 (mod n, x^2  x + 1)... Likely prime! real 8m29.679s user 15m1.912s sys 1m47.804s 

20180317, 03:45  #43  
Feb 2017
Nowhere
3·7·13^{2} Posts 
Quote:
Asymptotically, this is 6/pi^2 * N^2. Long known. The additional condition that a + b is odd, knocks out the pairs (a, b) with a and b both odd. In this case, b  a is even and gcd(b  a, b) = 1, so for odd b > 1, the condition knocks out exactly 1/2*eulerphi(b) pairs. For b = 1 it knocks out the pair (1, 1). I'm too lazy to work out the modified asymptotic. I'm sure it is long known, but alas I'm also too lazy to look it up ;) Last fiddled with by Dr Sardonicus on 20180317 at 03:53 

20180317, 04:28  #44 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9123_{10} Posts 

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