OFFSET
1,1
COMMENTS
No others < 1299709. Are there any others? Related to a conjecture of Goldbach.
The next element of the sequence, if it exists, is larger than 10^9 ; see A060003. - M. F. Hasler, Nov 16 2007
The next element, if it exists, is larger than 2*10^13. - Benjamin Chaffin, Mar 28 2008
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 226.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 137, p. 46, Ellipses, Paris 2008.
L. E. Dickson, History of the theory of Numbers, vol. 1, page 424.
LINKS
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.
Mark VandeWettering, Toying with a lesser known Goldbach Conjecture
MAPLE
N:= 10^6: # to check primes up to N
P:= select(isprime, {2, seq(i, i=3..N, 2)}):
S:= {seq(2*b^2, b=1..floor(sqrt(N/2)))}:
P minus {seq(seq(p+s, p=P), s=S)}; # Robert Israel, Jan 19 2016
MATHEMATICA
fQ[n_] := Block[{k = Floor[ Sqrt[ n/2]]}, While[k > 0 && !PrimeQ[n - 2*k^2], k--]; k == 0]; Select[ Prime[Range[238]], fQ] (* Robert G. Wilson v, Sep 07 2012 *)
PROG
(PARI) forprime( n=1, default(primelimit), for(s=1, sqrtint(n\2), if(isprime(n-2*s^2), next(2))); print(n)) \\ M. F. Hasler, Nov 16 2007
(PARI) forprime(p=2, 4e9, forstep(k=sqrt(p\2), 1, -1, if(isprime(p-2*k^2), next(2))); print1(p", ")) \\ Charles R Greathouse IV, Aug 04 2011
CROSSREFS
KEYWORD
nonn,more
AUTHOR
STATUS
approved