Problem 58379. Determine whether a number is prome

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161.042px 8px; transform-origin: 161.042px 8px; unicode-bidi: normal; "><span style="">In discussing the unique factorization of numbers in </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.9667px 8px; transform-origin: 85.9667px 8px; unicode-bidi: normal; "><span style="font-style: italic; ">Elementary Number Theory</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.992px 8px; transform-origin: 136.992px 8px; unicode-bidi: normal; "><span style="">, Underwood Dudley devised a new number system:</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 220.125px 8px; transform-origin: 220.125px 8px; unicode-bidi: normal; "><span style="">“Consider the integers 1, 5, 9, 13, 17,…; that is, all integers of the form </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="4n+1" style="width: 42.5px; height: 18px;" width="42.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; "><span style="">, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="n = 0, 1,..." style="width: 71.5px; height: 18px;" width="71.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5583px 8px; transform-origin: 95.5583px 8px; unicode-bidi: normal; "><span style=""> We will call an element of this set </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.7833px 8px; transform-origin: 21.7833px 8px; unicode-bidi: normal; "><span style="font-style: italic; ">prome </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.742px 8px; transform-origin: 128.742px 8px; unicode-bidi: normal; "><span style="">if it has no divisors other than 1 and itself </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; "><span style="font-style: italic; ">in the set</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.517px 8px; transform-origin: 115.517px 8px; unicode-bidi: normal; "><span style="">. For example, 21 is prome, whereas </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="25 = 5*5" style="width: 62.5px; height: 18px;" width="62.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.0917px 8px; transform-origin: 23.0917px 8px; unicode-bidi: normal; "><span style=""> is not."</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.858px 8px; transform-origin: 253.858px 8px; unicode-bidi: normal; "><span style="">Write a function to determine whether a number is prome. Take 1 to be not prome.</span></span></div></div></div>

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Christian Schröder on 1 Jun 2023

Underwood Dudley seems to be prone (prome?) to joking -- as befits anyone bearing such a cromulent name --: these are usually called Hilbert primes or S-primes instead.

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Problem 58379. Determine whether a number is prome

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