A094494
Primes p such that 2^j+p^j are primes for j=0,2,4,8.
Original entry on oeis.org
6203, 16067, 72367, 105653, 179743, 323903, 1005467, 1040113, 1276243, 1331527, 1582447, 1838297, 1894873, 2202433, 2314603, 2366993, 2369033, 2416943, 2533627, 2698697, 2804437, 2806613, 2823277, 2826337, 2851867, 2888693, 3911783, 4217617, 4432837, 4475473
Offset: 1
Conditions mean 2,p^2+4,16+p^4,256+p^8 are all primes.
-
p:= 2: count:= 0: Res:= NULL:
while count < 30 do
p:= nextprime(p);
if isprime(4+p^2) and isprime(16+p^4) and isprime(256+p^8) then
count:= count+1;
Res:= Res, p;
fi
od:
Res; # Robert Israel, Jul 17 2018
-
{ta=Table[0, {100}], u=1}; Do[s0=2;s2=4+Prime[j]^2;s2=16+Prime[j]^4;s8=256+Prime[j]^8 If[PrimeQ[s0]&&PrimeQ[s2]&&PrimeQ[s4]&&PrimeQ[s8], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]
Select[Prime[Range[210000]],AllTrue[Table[2^j+#^j,{j,{0,2,4,8}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 13 2017 *)
A094492
Primes p such that 2^j+p^j are primes for j=0,1,4,16.
Original entry on oeis.org
179, 461, 521, 1877, 4259, 9767, 30389, 33071, 33329, 93701, 120077, 124247, 145547, 163481, 181871, 245627, 344171, 345731, 487427, 492671, 522281, 598187, 700199, 709739, 736061, 769259, 833717, 955709, 966869, 1009649, 1030739
Offset: 1
For j=0 1+1=2 is prime; other conditions are:
because of p^1+2=prime; 3rd and 4th conditions are as
follows: prime=p^4+16 and prime=65536+p^16.
-
{ta=Table[0, {100}], u=1}; Do[s0=2;s1=2+Prime[j]^1;s8=16+Prime[j]^4;s16=65536+Prime[j]^16 If[PrimeQ[s0]&&PrimeQ[s4]&&PrimeQ[s8]&&PrimeQ[s128], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]
With[{j={0,1,4,16}},Select[Prime[Range[81000]],And@@PrimeQ[2^j+#^j]&]] (* Harvey P. Dale, Oct 17 2011 *)
A094493
Primes p such that 2^j+p^j are primes for j=0,1,2,16.
Original entry on oeis.org
43577, 84317, 93887, 108377, 124247, 346667, 379997, 431867, 461297, 579197, 681257, 819317, 863867, 889037, 1143047, 1146797, 1271027, 1306817, 1518707, 1775867, 1926647, 1948517, 2119937, 2177447, 2348807, 2491607, 2604557
Offset: 1
For j=0: 1+1=2 is prime; other conditions are:
because of p^1+2=prime; 3rd and 4th conditions are as
follows: prime=p^2+4 and prime=65536+p^16.
-
{ta=Table[0, {100}], u=1}; Do[s0=2;s1=2+Prime[j]^1;s2=4+Prime[j]^2;s16=65536+Prime[j]^16 If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s16], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]
Select[Prime[Range[2*10^5]],AllTrue[Table[2^k+#^k,{k,{0,1,2,16}}],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 05 2021 *)
Showing 1-3 of 3 results.
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