Near-square prime - Revision history

Vipul at 23:16, 1 August 2012

2012-08-01T23:16:48Z

← Older revision		Revision as of 23:16, 1 August 2012
Line 10:		Line 10:
	! 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
	\|-		\|-
	\| -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"/>
	\|}		\|}

Vipul: /* Occurrence */

2012-08-01T23:16:03Z

Occurrence

← Older revision		Revision as of 23:16, 1 August 2012
Line 10:		Line 10:
	! 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
	\|-		\|-
	\| -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"/>
	\|}		\|}

Vipul: /* Occurrence */

2012-08-01T23:15:53Z

Occurrence

← Older revision		Revision as of 23:15, 1 August 2012
Line 10:		Line 10:
	! 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
	\|-		\|-
	\| -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"/>
	\|}		\|}

Vipul: Created page with "==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 c..."

2012-07-03T18:30:35Z

Created page with "==Definition== A '''near-square prime''' of type <math>n^2 - k</math> for fixed <math>k</math> is a prime that can be written in the form <math>n^2 - k</math>. Note that we c..."

New page

==Definition==

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

According to the [[Bunyakovsky conjecture]], for any fixed <math>k</math> not a perfect square, there should be infinitely many near-square primes of the form <math>n^2 - k</math>.

==Occurrence==

{| class="sortable" border="1"
! 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"/>
|}

Near-square prime - Revision history

Vipul at 23:16, 1 August 2012

Vipul: /* Occurrence */

Vipul: /* Occurrence */

Vipul: Created page with "==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 c..."

Vipul: Created page with "==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 c..."