Is there an Infinite Number of Primes of Form n^2 + 1?
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Open Question
Is there an infinite number of prime numbers of the form $n^2 + 1$?
Also known as
This problem is found according to some sources to be referred to as the Fifth Hardy-Littlewood Conjecture, but it is difficult to find hard evidence to back this up.
Landau's Problems
This is the $4$th of Landau's problems.
Sources
- 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.): $\text {II}$: The Series of Primes ($2$): $\S 2.7$. Further Results on formulae for primes: $\text {(iii)}$
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,3727 \ldots$