OFFSET
1,1
COMMENTS
Conjectured to be infinite.
REFERENCES
G. H. Hardy and W. M. Wright, Unsolved Problems Concerning Primes, Section 2.8 and Appendix 3 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, p. 19.
P. Ribenboim, The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 206-208, 1996.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Landau's Problems.
EXAMPLE
11 is a term because 10^2+1=101 and 5^2+6^2=(1/2)*(11^2+1)=61 are primes.
MAPLE
a:=proc(n) if isprime(1+(n-1)^2)=true and type((n^2+1)/2, integer)=true and isprime((n^2+1)/2)=true then n else fi end: seq(a(n), n=1..3000); # Emeric Deutsch, May 31 2005
MATHEMATICA
Select[Range[2, 2500], PrimeQ[1+(#-1)^2]&&PrimeQ[(1/2)*(#^2+1)]&] (* James C. McMahon, Jan 10 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Garcia, Feb 09 2005
EXTENSIONS
More terms from Emeric Deutsch, May 31 2005
STATUS
approved