Problem 57869. Identify de Polignac numbers

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: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; "><span style="">The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="125 = 109+2^4" style="width: 96px; height: 19px;" width="96" height="19"></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: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; "><span style="">, and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="329 = 73+2^8" style="width: 88.5px; height: 19px;" width="88.5" height="19"></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: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; "><span style="">. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.</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: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; "><span style="">Write a function that determines whether an odd number is a de Polignac number. </span></span></div></div></div>

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Problem 57869. Identify de Polignac numbers

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