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A125779
Numbers n such that n^4 + 1, n^4 + 3, n^4 + 7 and n^4 + 9 are all prime.
4
83270, 519370, 939220, 1844170, 2263910, 2293460, 2429260, 2595980, 3133640, 3216530, 3474200, 3559760, 4787050, 5306720, 5505940, 6238780, 6889430, 6932770, 7320160, 8286340, 8427880, 8744290, 8961590, 9863440, 10871530
OFFSET
1,1
COMMENTS
Schinzel proved in 1958 that the set of primes of kind n^(2^k) + 1, n^(2^k) + 3, n^(2^k) + 7 and n^(2^k) + 9 is infinite for each number k > 0.
REFERENCES
Sierpinski, W. Elementary theory of numbers. Warszawa 1964 Monografie Matematyczne Vol. 42.
LINKS
MAPLE
R:= NULL: count:= 0:
for k from 0 while count < 30 do
for i in [20, 30, 40, 50] do
n:= 70*k + i;
if isprime(n^4+1) and isprime(n^4+3) and isprime(n^4+7) and isprime(n^4+9) then
count:= count+1; R:= R, n;
fi
od od:
R; # Robert Israel, Feb 11 2021
MATHEMATICA
Select[Range[109*10^5], AllTrue[#^4+{1, 3, 7, 9}, PrimeQ]&] (* Harvey P. Dale, May 15 2022 *)
CROSSREFS
Sequence in context: A190385 A201251 A235097 * A233925 A032752 A104928
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 09 2006
EXTENSIONS
Corrected and extended by Donovan Johnson, Apr 22 2008
STATUS
approved