Problem 57412. Easy Sequences 85: Hyperprimorials

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>, the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Primorial\"><w:r><w:t>primorial</w:t></w:r></w:hyperlink><w:r><w:t> of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R_n</w:t></w:r></w:customXml><w:r><w:t>, is defined as product of all primes from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t> to the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-th prime. In other words, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p_n</w:t></w:r></w:customXml><w:r><w:t> is the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-th prime number: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R_n=p_n \\cdot p_{n-1} \\cdot p_{n-2} \\ ...\\ p_{3} \\cdot p_{2} \\cdot p_{1} </w:t></w:r></w:customXml><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For this problem, </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>we want to calculate the hyperprimorial of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, which we will define as: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_n=p_{n}^{p_{n-1}^{p_{n-2}^{{\\ \\cdot}^{{\\cdot}^{{\\cdot}^{p_{3}^{p_{2}^{p_{1}}</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_3 = p_3^{p_2^{P_1}} = 5^{3^2}=5^9=1953125</w:t></w:r></w:customXml><w:r><w:t>; and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_4 = p_4^{p_3^{p_2^{P_1}}} = 7^{5^{3^2}}=7^{1953125}=128647942\\ ...\\ 431920807</w:t></w:r></w:customXml><w:r><w:t> (with 1,650,583 digits).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>From what we see above, calculating hyperprimorial will quickly involve extremely large integers, as such, </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>please return only the last 6 digits of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_n</w:t></w:r></w:customXml><w:r><w:t>. Therefore, </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>in the example above the final output should be: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_3=953125</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>H_4=920807</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>-----------------------------</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>NOTE: </w:t></w:r><w:r><w:t>OEIS's \"hyperprimorial\" sequence, </w:t></w:r><w:hyperlink w:docLocation=\"https://oeis.org/A076265\"><w:r><w:t>#A076265,</w:t></w:r></w:hyperlink><w:r><w:t> is not the same as what is defined in this problem.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<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: 398px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 199px; transform-origin: 407px 199px; vertical-align: baseline; "><div style="block-size: 44px; 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 22px; text-align: left; transform-origin: 384px 22px; 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: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; ">Given an integer n<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: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; ">, the <a target='_blank' href = "https://en.wikipedia.org/wiki/Primorial">primorial</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: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; "> of n<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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,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" style="width: 17px; height: 20px;" width="17" height="20"><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: 128px 8px; transform-origin: 128px 8px; unicode-bidi: normal; ">, is defined as product of all primes from 2<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: 22px 8px; transform-origin: 22px 8px; unicode-bidi: normal; "> to the n<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: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; ">-th prime. In other words, if <img src="data:image/png;base64,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" style="width: 15.5px; height: 20px;" width="15.5" height="20"><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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "> is the n<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: 60px 8px; transform-origin: 60px 8px; unicode-bidi: normal; ">-th prime number: <img src="data:image/png;base64,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" style="width: 206px; height: 20px;" width="206" height="20"><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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; "> .</div><div style="block-size: 79px; 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 39.5px; text-align: left; transform-origin: 384px 39.5px; 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: 55.5px 8px; transform-origin: 55.5px 8px; unicode-bidi: normal; ">For this problem, <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: 148.5px 8px; transform-origin: 148.5px 8px; unicode-bidi: normal; ">we want to calculate the hyperprimorial of n<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: 96.5px 8px; transform-origin: 96.5px 8px; unicode-bidi: normal; ">, which we will define as: <img src="data:image/png;base64,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" style="width: 95px; height: 79px;" width="95" height="79"><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: 4px 8px; transform-origin: 4px 8px; 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: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; ">For example:</div><div style="block-size: 37px; 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 18.5px; text-align: left; transform-origin: 384px 18.5px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 202px; height: 37px;" width="202" height="37"><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; ">; and</div><div style="block-size: 47px; 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 23.5px; text-align: left; transform-origin: 384px 23.5px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; "> <img 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ICQ9iwYJAE14soytUil37xJN4bynVanyoEAz9fICe57cjxGv1adoN/7okmPSEf6La2+OSD/vP0Clw6/MheRXrqPYOWO1nQMmMAA1ihetbrkGBLVc6/+/Ngy1OLm6yFjmEFZcfUsZL2VOw7MNeOGJ19Z40dGZ+g7pY6W2Fbn1Mkb71oklIYOjLelu5Nf5elF7sGY8+8HxRGPH1dEetm/towKnPC0NtZiLMS388cmMMigjV1pAiszyTomrFcUgPb2LuBR3+7KvRL8HmvpMhsQWkwyyv0vY/OdPO5HPr1QvFz6jDbv+IbR68DmbMx7SYvL7WhE2c5yq9ignWHJJTrpDINtedxzCxMOVHsKRcbIBtHSW2YDZc+SWiMBnsT0+pXopEIudzOySav+hlh6uWT32sMg0vuOIv2W/A1mrIfQH4PyX5i0Nn76dMoB3luqWsS6NzEqB9+hFlKPPwknJjOMNlLqxKg5Ld9wptfaiOnbdau8fpysRTsZqvPUOlpyG51DN7RPLJvT4tkioSDGreV8z4UyLlfQm31ORHo5KWw95/MuLafoWyG1ybmfYEGfsj16Mt1aZWnpxhWLXtk40SjxGpvv5HE/Q3qHWm69VVgRBub4XJ+eBgeQzBLL/LkvJ0W0y5bvJrUcihXb+p7aLchGZsMCZuy4WjF4fQdfG8S9NR0rFbAO4ALx8DGray2MHX7PxQHv+c2J9MH26WVJL60QF+3lzOaVrH7L+Xp+rEmW9OJbg3tCa5JJqydSLldLvLWo9W3xmdoqlh+4e8u0GXxRjktNYAGDdQxXjfRiE1FU96143fx/b9XIj6uRASOjM8oxpY4y2K31GY4DmAxjlQIrpjWiRutob1wp3bEiTDKk108Ke2Sa3Mpbe+nu05ugedeHMn1aYnvW2tYEjYS29y6fKVdax+Y7edzPkF5f4GjQKa3C0Qw2ajC6X0cADQkfaLlUIbyejsBQCxwH3j2R3kyb4dJbNNHKkkrmWYuO0NIHaUf9D97tPZfVD1aTD5qUy5s9rLL6ZfA+5TNZ0otxgEunLf04wJVkzxNiDJC1PQm9tjBkDOphR1cYWO9BalukN4M/y1RbbuaA3iO9fiLQs5QN0XlKHWXKvMZnOIHFRkJMhNlGI8trrazkN9Ek3b+bIb3eRapHer17Bidq6Jt/xqS34unbmk/f+633VuW9fp68ejJdcx/034i3Ik/NN2qH3XE/Q3r5ASOjiAx4cHrsP1J6Dff9hpb/OAyQnCleZn9jw9M/mAwJU5ItNxq/IjjEaHFmHLnkMCV+jJqsPR1bko7IfzpLKpE6N9ygf4lcCNh5Rv0P0oUOLT0z+mWXzzxCQ/SLW+1pn8iS3oxWHJRrkyNPXEv3BL+RpmwLnjBDB37L3IiaWaXAe8yDEVo8EYh8mWtlp6W2tzmzR3q9gaj13Nw6oxy9OsrU8dqeQbsD1owPPoX08lvJ9EPEKUN6/TfYI73+G8q6V0AP39a961c2X/++b++lkbPEhfqWKxlT843aYHfcj0ivN7sjo4gMcFkHz0ZLNpHirfs+Bt3YNPDe2NiQaADljn8MstjhidBu2J38chPucB7SODPl4VLfb9rDQyxRmbSnPMNBaEoaeDdaUsymz7Y7ZPKFjxT+v5F/a1aHMc+du33XdKZrQ7SzPkMqkT7aMAYfEJgyTFwtf/rXRj6W+DY/Z9LSM9IP9Q8C4g/KgD5IF9EkWtaUrH6+bEup5zlJLwebWp/HOucRz8AZdY/T7+ArjLGjduSzN6TAwgaL3c0mPoIE/h+FAIP1Hn68rNuppJdjXY0AsZ2hvntjJp9rkd65dYY+vToa018t+R1GUPARCcaSXu6nGTruDiW9vdWsLFks64QTtNJC7flaj6f4b6UcT72bDvLlZjqUA996bUPgHPm22l047kekt7Tc/nbQwjHgsDM61mYgX/FTPrgxs3ufX7lxA/duNEEosXIW3/OD7JUBHRTEO9ZjYMZVGyCm4DH1Xb/0MjatOSMn9JY4aiGD8PG+xwQ+pucMR7aU9s06zLo2eItcb6BHp/Rnh8QRfs+vhLC/QefMgYo+axftf5wQ0QLmiRJJFdKukdNIP7QXRCBAp41VGl6YzKJNwAKJ3dD3mET6Zdr/Uup5LtLrl35blvuS+AInfPM9IuEHSDyP+sEBFP9j8nwTvzu9RRhQt9DJu1VMIb091wbo6PvCnlWwR3rn1hl6Zeoo03bX8AxXksq43UNJL/oaxJrlpke01yj2rMcnQ3p7pNKnNZb0tiyuvp1mSW9tjC6JL3SG+wj5UNle5sq31g5Dl8aI9JYdzpDGHqU9JC3/LAC+OPZl914UrDnKwm9WgAWhtA76ih07ASiXBB+3fP7eZEkWXuKExvayCLTg/n9XcBybZG+Joww8joH030zGBLgfq1/rvaW0b+qXcW0Anm834cCADu8uk/KgjzccEv1r+1k7rKYcYJAOrMwgsZ4cY0CDXgzhh/pDZ/yXxXMsQ6RfrdP29UP/v6x+mTaxlHqei/QynWhlq0V8W1EhfEzOjAW5JJm0/pfpTyG9PdcG1L03FmV245dE4hg6Q69sHWXa79KfabkADiG9HNMQdrU88CGzvwAYZUgvnvNupJmIH9F3xvrhyjDSL1fKaj7CrXqNViVqfWgrrOCc+Zb6hi6NETH1yzQRcfOdZ7ThZekfTEa/aLNCdrafyUvPDEMgXOIYltyun866NkQgoU6O4d8e5av7fQTmIL0cWOHaRd/JVq7MDwMiLOveTaHnKgBi2HJb8Rtj/NhDvWqWuSmkt+fagHJz8xSJUq1c3qDhl4yPpfOQOlr7N4M2hvBkNXeoIaTX41AeLoV7mdXiLOn1E6VaSD6ubtUOUerVF7+3Gn/LGuZ6kVmQN1fveGAWjRG4VyvLXPmW5U6N+z3S6zsFJB4R5GhGvvYPyevvsWn5LvuKzW6k2hJG5yxLuMRxTuVWlHfWtWFFRZKqBQJzkF6QQPRxtagMPjsSPZLA0mKPZ8vBObIwMX3/HN3JGHqqXIXDO2NJb+TaQH3oluNP8eLpXiD7Pk6w3xx0DJ2hU7aO1v6BkPi0COlY0ktcfMSCzL6lLOlF+j5tTPLoavUa+x3tjoc84NkMpyAWrY29c7gZkIz7kxZB4LG/iQS9NILOkW+tnabG/R6R9RUQhfcod9hmZkCskCE7IZfyQWYGimxnvZQybUmPcIljS4U9Ylkyrg1HzF5JnwCBTF/WU4MhtfxmodrzzKc2lnirZxmnN1pRY17lkukrDwMv/IXh/1te2JgI/2xcIAXfOfwebXCOXBt8Pozm88v2TxB8uG89YQI3qmtN3nd4mGMgycLcOmfr6ATN7ahZ0MKOCcUnGzl91P6PFQMQMfiD4/qhSXYVynOdiBch7SGkF8+DF8FSCqKLCy6N/2QCd7CnDv/LbM4mFtCx3JhLaLI+wn6C6MvM1QOQ25LzlZZpT7yn5ttqRKlxv0d6h1hu/fJSdjMS0x9Kepew65m6t44D9nhkfX+O2hucIHE08mfOkM/U6A38QDMdwwzqzp7EEto3CsUODb9HURtmB2EHCS6lnqeQXhBAEIeI8KI6SV5b/b3fP+KtvSSzGFd6G4JL0ovT+fwya7ZJRQYb5jN03PL5e7Lgd9T7MmT1xXM9nYfU0ZA8l/hsuTqd1TFDXn1aQ6zFQ0lvS+csUWTfDR19tJJaut4PN7uRzfMZumS0xloaNpG3t/ZOzbdWlvS43yK9Qy23fqaeaUDe/D208zj3rmePTWt5w3fgUZi37Ie59OfGdti+XNkJUw+L1k7VpeNH/c7dvqkHO6Y9+Oefo20spZ7Hkt4hZCrjSuAHSD8A+xXHHrkryfG7rVJ7G2vRjzN8GgZt+iP2Njgz+kFEwKP25DEvg/3PqfOQOop0XsN9tCEeRd7S9+V2A5ZJ1CGW5HHB7aR2gmMrDba1zGayOUivnyS1DnehrtwoGhFePO+jTPV4m2+vnq9lyL/f8I9woHPkW6uX9LjfIr1DLbc0K0OZKIA9gAbAsJbCt2ko6cWHfHGGL3Bs9AaPTc05vNV5z6DyopNYSvQGWpQyPk9LBPTc7ZuYsLOKvuclYrgGnZZSz2NIby3+aYk5+kEsGyP8X4b04n0SBE8mfH/aa4scg7IrPFmdfLlo2eqdXhW1PV+ejIHIpzdE56F1FOm9lfsZohaVFW0NBC6zAjYH6fVGtGglooztXCsL2sZDhxvEo7VqjceYfxnnN4Ml+5fSoDUl31qZ0uN+i/R6y230gZenckRkA4W9zwSnlmFWNpT0Rg3y2Pe95aHEz4fjyXRoGb+bY5dnS+lzQtL7gLdU3mOVxa9mRN/zsXRQuqdBYCjppa9e71AR9oM+5jUHpRZx7bU5upO1CK1/NztJG0IgWRPUI5tHWYM+qkNtV3tU41mdx9ZRlH/rPsr1JhPEt+ZGPP8s9H6VSS0kZPTuWJ1a72WIWi9P1kHWbXEq6fVRHSKuBN7mT5+rlQOTbfiYw+iHy7epmhHPf1ulZdvHVUdYt9pFvlTyyCn5lvkMGvdbpHeI5bY8MadVeCjKeJkIWgxH/jWS3p5FgZOFDOEFHr3z5uf+2PeQHvHPdkh7wGRMGenakLWajclD7ywDgSGkl2QKk8rPdNRHuCj0kz58GfNpLc9yHKn1nX6ArBFOpj3EFSdLIFlM79qQsfCV8PhoDr3A/b1WkdF5Sh2NbZHeSFa6/EUHNfXeHatP770e6eWBFnB/qMWYrUUqiHScQnrJD2AlxeZGWmdrefqxzx+u45+9YH9gdb0kt8yn9u31vi3vdlH7Lv0kr2ahHptvWf5B436N9HoSi8R7fivlDr2evwkB4Gk9BDOavUSN6pT3/Qfsy8rQO/AXihon9fXYiaTNU4u0JkUxpefJbbupcDkrE5Jnuyhsv2Tot+D7x7Bavfou+/oInVq/zkEOfac/jY97PKBL6xQnTMQwuIGQYIDl4SaeLLferemaIZD+PeYzhFjzfYx1Nx/+GHKaV6l3pPMcdRTVa+2+X34vxzLvzgHyVk4Yeu+O0SV6JyK9mNDxgr4MG3bBfgd3ucOkdRx5mbefUCLd1kmF5Xv0TcZGTBBRhP/qRZfwE4eo/C1DhieOd1oi8HH3bf5th//VdH3Q/ok+BFwR1nyeSos0I040Nl+vx6Bx35NedICwvtYc6RE2489NeDwrnsVyBsNqeAUYlqV0DEfjRrgW/n+NpNfvOuQpUCz70JPSsFQGawms3SK90aca32dHMeepbnGu23wCAwOusX7v20RlO6Xq9fXo4zHAlgM7+u9LkxDgG2wR0NrYgY1EXzaJIrdwKRynq1GX7Lul6n7TU6adc8/CxyyhnsUN+UBPHIzwiyawrGHD1GdNSAiSMP7EY5HOc9XRUP1Q3ltMQBJJmHwaXOG9v4Jd9O5QXaLnWY+tzWuYWPyGCdopLvKZJxP1zrzBE3D6ZO17Qb6YOJUkFnX7SpNfMwFRBL942CT6JoDtTVGh3f377PeaCwoeQdmvNiEHHHICLN0miBv7kUybn5Lv4HE/OnBiAJbdR1GoD5j42cIaSa+flU7BDmW/YIJYgo+ZiPTO1dKUjhAQAkLgvAhg4L/S5JsmUdzf82qq3JeCAEgj4kn/p0k2ZvBSdF+VHlOI25CCwr8LywLoBHhhNoVZMJbUMMtfQ+dAM/qYJS6Wm9ErsMnjeSK9Q5qRnhUCQkAICAEhIASEwDgETkV66czd03Lpvr3eN2mKryOWjrlENnQn6Lha1ltCQAgIASEgBISAENg5AqcivTWY1+be4J3Sx26UgmM4/NHo7ybSu/MPUMUXAkJACAgBISAEToOASG8OZx/KBG+MIb1l9AqkI9Kbw19PCQEhIASEgBAQAkJgEgIivTF8DKxde3LI0YUIzYELm9d4XW6/3GOCsCR3mXzXhBEyYs30hBAQAkJACAgBISAEhEAKgXOS3pSCG3qI8QF7RVIUhw1VuIoiBISAEBACQkAILAcBkd7z1oXcG86Lv3IXAkJACAgBISAEdoKASO95KzTxbGwAAADBSURBVFqk97z4K3chIASEgBAQAkJgJwiI9J63okV6z4u/chcCQkAICAEhIAR2goBI704qWsUUAkJACAgBISAEhMCeERDp3XPtq+xCQAgIASEgBISAENgJAiK9O6loFVMICAEhIASEgBAQAntGQKR3z7WvsgsBISAEhIAQEAJCYCcIiPTupKJVTCEgBISAEBACQkAI7BkBkd49177KLgSEgBAQAkJACAiBnSAg0ruTilYxhYAQEAJCQAgIASGwZwT+DyVgptdbGFtwAAAAAElFTkSuQmCC" style="width: 350.5px; height: 47px;" width="350.5" height="47"><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: 73.5px 8px; transform-origin: 73.5px 8px; unicode-bidi: normal; "> (with 1,650,583 digits).</div><div style="block-size: 65px; 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 32.5px; text-align: left; transform-origin: 384px 32.5px; 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: 331.5px 8px; transform-origin: 331.5px 8px; unicode-bidi: normal; ">From what we see above, calculating hyperprimorial will quickly involve extremely large integers, as such, <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: 49.5px 8px; transform-origin: 49.5px 8px; unicode-bidi: normal; ">please return only the last 6 digits of <img src="data:image/png;base64,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" style="width: 19px; height: 20px;" width="19" height="20"><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: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; ">. Therefore, <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: 172px 8px; transform-origin: 172px 8px; unicode-bidi: normal; ">in the example above the final output should be: <img src="data:image/png;base64,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" style="width: 82.5px; height: 20px;" width="82.5" height="20"><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: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 82.5px; height: 20px;" width="82.5" height="20"><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: 2px 8px; transform-origin: 2px 8px; 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: 72.5px 8px; transform-origin: 72.5px 8px; 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: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">NOTE: <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: 110px 8px; transform-origin: 110px 8px; unicode-bidi: normal; ">OEIS's "hyperprimorial" sequence, <a target='_blank' href = "https://oeis.org/A076265">#A076265,</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: 158.5px 8px; transform-origin: 158.5px 8px; unicode-bidi: normal; "> is not the same as what is defined in this problem.</div></div></div>

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Problem 57412. Easy Sequences 85: Hyperprimorials

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Problem 57412. Easy Sequences 85: Hyperprimorials

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