# Difference between revisions of "Near-square prime"

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! Value of <math>k</math> !! Polynomial <math>n^2 - k</math> !! First few prime values | ! Value of <math>k</math> !! Polynomial <math>n^2 - k</math> !! First few prime values | ||

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− | | -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"/> | + | | -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"/> |

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## Latest revision as of 23:16, 1 August 2012

## Definition

A **near-square prime** of type for fixed is a prime that can be written in the form . Note that we consider near-square primes for *not* a perfect square, because if is a perfect square, then factorizes algebraically.

According to the Bunyakovsky conjecture, for any fixed not a perfect square, there should be infinitely many near-square primes of the form .

## Occurrence

Value of | Polynomial | First few prime values |
---|---|---|

-1 | 2, 5, 17, 37, 101, 197, 257, [SHOW MORE]View list on OEIS |