Problem 46046. Determine whether a number is a cluster prime

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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; 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: 4.66667px 7.91667px; transform-origin: 4.66667px 7.91667px; unicode-bidi: normal; ">A<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> <a target='_blank' href = "https://mathworld.wolfram.com/ClusterPrime.html">cluster prime</a><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: 75.4667px 7.91667px; transform-origin: 75.4667px 7.91667px; unicode-bidi: normal; "> is an odd prime number<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> p<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: 150.533px 7.91667px; transform-origin: 150.533px 7.91667px; unicode-bidi: normal; "> such that all even numbers less than or equal to<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" alt="p-3" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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: 74.3px 7.91667px; transform-origin: 74.3px 7.91667px; unicode-bidi: normal; "> can be expressed as a difference of two primes<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> q<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: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; "> and<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAkCAYAAACe0YppAAABJ0lEQVRYhe2WYQ2DMBCFPw84qAEMoAAFOMABDmahGpAwD7OABiywH+2lt6VsZBwlS/gS/tCmL717fS1cXPwpNVCVFu2BBbiVFn5E4a6kqIuiE4VLLWXuS4oCjJyw24qTdtsSjGWGIzh04PNufBQ3EfSE8nmgieIemNV/ocKgt3VcfI6CGjmnS2ZsF+0HUYB7FJ0xdK8jlXGtnzI+WolC2s2aO2tSmc0isVWLrrnTqznOSngk9S6H5PBCqIwZsuha70Y1Z7ASbdSiuXu0U+MLodfmwv5trCME/7dW/IQEvNylDaGnA+k859LKhIHXcsqxcmxz/C5q0mWg+yjHyDSttnBIWn1DG6/oJX/jgLTawkRy++FUhBLrtJo4yNEaeW3kvqIP9YufeQJgwmvH4HW5FwAAAABJRU5ErkJggg==" alt="q'" style="width: 15px; height: 18px;" width="15" height="18"><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: 70.8px 7.91667px; transform-origin: 70.8px 7.91667px; unicode-bidi: normal; "> that are no larger than<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> p<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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; ">.</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: 204.467px 7.91667px; transform-origin: 204.467px 7.91667px; unicode-bidi: normal; ">Write a function to determine whether a number is a cluster prime.</div></div></div>

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Last Solution submitted on Feb 13, 2021

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Solution 2691218

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Gifari Zulkarnaen on 14 Jul 2020

Very nice problem

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number theory primes

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Problem 46046. Determine whether a number is a cluster prime

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Problem 46046. Determine whether a number is a cluster prime

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