Near-square prime: Difference between revisions

Latest revision as of 23:16, 1 August 2012

Definition

A near-square prime of type $n^{2} - k$ for fixed $k$ is a prime that can be written in the form $n^{2} - k$ . Note that we consider near-square primes for $k$ not a perfect square, because if $k$ is a perfect square, then $n^{2} - k$ factorizes algebraically.

According to the Bunyakovsky conjecture, for any fixed $k$ not a perfect square, there should be infinitely many near-square primes of the form $n^{2} - k$ .

Occurrence

Value of

k

Polynomial

n^{2} - k

First few prime values

-1

n^{2} + 1

2, 5, 17, 37, 101, 197, 257, [SHOW MORE]View list on OEIS

@@ Line 10: / Line 10: @@
 ! Value of <math>k</math> !! Polynomial <math>n^2 - k</math> !! First few prime values
 |-
-| -1 || <math>n^2 + 1</math> || <section begin="plus-one-list"/>[[2]], [[5]], [[17]], [[37]], [[101]], [[197]], [[257]], <toggledisplay>401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177</toggledisplay><section end="plus-one-list"/>[[Oeis:A002496|View list on OEIS]]<section end=plus-one-list"/>
+| -1 || <math>n^2 + 1</math> || <section begin="plus-one-list"/>[[2]], [[5]], [[17]], [[37]], [[101]], [[197]], [[257]], <toggledisplay>401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177</toggledisplay>[[Oeis:A002496|View list on OEIS]]<section end="plus-one-list"/>
 |}