20180315, 17:26  #12  
Sep 2002
Database er0rr
D6C_{16} Posts 
Quote:
Edit: I ran PFGW for bases less than or equal to 50 and found no PRP: Code:
cat Jeppe.abc2 ABC2 $a^16384+$b^16384 a: from 2 to 50 step 2 b: from 3 to 50 step 2 Code:
./pfgw64 f N Jeppe.abc2 Last fiddled with by paulunderwood on 20180315 at 18:24 

20180315, 19:00  #13  
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
Quote:


20180316, 06:18  #14 
"Jeppe"
Jan 2016
Denmark
240_{8} Posts 
See A291944 in OEIS; it is not public yet, so see its history.
I used PARI/GP ispseudoprime in a loop, like the code shown there, and I suspect Robert G. Wilson v used Mathematica. Maybe PFGW is faster? There is no point in all of us running the same tests, except whoever uses the best tools will "win" the competition. I just thought maybe this had been established already. /JeppeSN 
20180316, 08:30  #15  
Jun 2003
2·13·181 Posts 
Quote:
PFGW should indeed be faster than Pari or Mathematica. EDIT: Testing 71^16384+46^16384, PFGW took about 20s, while Pari took 2mins and change. So PFGW is about 6x faster. Last fiddled with by axn on 20180316 at 08:33 

20180316, 10:33  #16  
Sep 2002
Database er0rr
2^{2}·859 Posts 
Quote:


20180316, 10:36  #17 
"Jeppe"
Jan 2016
Denmark
2^{5}·5 Posts 
Something to note:
Use here the convention \(a > b > 0\). There is a slight chance that the smallest odd prime \(a^{16384}+b^{16384}\) does not minimize \(a\). As an example, \(677 < 678\), but still \(677^{128}+670^{128} > 678^{128}+97^{128}\) (both of these sums of like powers are prime). However, for the smallest one with that exponent, \(27^{128}+20^{128}\), the value \(a=27\) is also minimal. And I think this will be the case generally, because the bases \(a\) and \(b\) will be relatively small (I conjecture). But we will check for that with 16384 once axn's excellent initiative has come to fruition. /JeppeSN 
20180316, 12:19  #18  
Einyen
Dec 2003
Denmark
B95_{16} Posts 
Quote:
I used fbncsieve to sieve the factors k*2^14+1. It took only ~2min up to k=10^9. Then I used these prime factors in a quickly written GMP program to sieve an array 1000x1000 of a,b. First I removed all values where b>=a, a<2, b<2, a%2=b%2 (both odd or both even), and gcd(a,b)>1. Down to 61K candidates at k=462M. I'm running pfgw while continuing to trial factor. So far no PRP in 2<=b<=16 and b<a<=1000. 

20180316, 13:15  #19  
Jun 2003
2·13·181 Posts 
Quote:
Quote:
2<=a<=1000, 1<=b<a Last fiddled with by axn on 20180316 at 13:15 

20180316, 13:51  #20 
"Rashid Naimi"
Oct 2015
Remote to Here/There
19·101 Posts 
Stating the obvious for the sake of having it stated
a+b  a^q + b^q for all odd q And a+bi  a^q + b^q for all even q So the result will be definitely not prime over the imaginary field. Corrections are welcome. 
20180316, 13:53  #21  
"Jeppe"
Jan 2016
Denmark
2^{5}×5 Posts 
Quote:
Code:
(2,1) (3,2) (4,1) (4,3) (5,2) (5,4) (6,1) (6,3) (6,5) (7,2) (7,4) (7,6) (8,1) (8,3) (8,5) (8,7) . . . . . . /JeppeSN 

20180316, 14:21  #22 
Jun 2003
2×13×181 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is there a prime of the form......  PawnProver44  Miscellaneous Math  9  20160319 22:11 
OEIS A071580: Smallest prime of the form k*a(n1)*a(n2)*...*a(1)+1  arbooker  And now for something completely different  14  20150522 23:18 
Smallest prime with a digit sum of 911  Stargate38  Puzzles  6  20140929 14:18 
Smallest floor of k for cullen prime  Citrix  Prime Cullen Prime  12  20070426 19:52 
Smallest tenmilliondigit prime  Heck  Factoring  9  20041028 11:34 