See Carol number on Wiktionary
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"etymology_text": "First studied by Cletus Emmanuel, who named it after a friend, Carol G. Kirnon.",
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"examples": [
{
"ref": "2009, The Philosophers' Magazine - Issue 47, page 4:",
"text": "Mathematically, it is actually interesting in all sorts of ways, being both a Keith number and a Carol number.",
"type": "quote"
},
{
"ref": "2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, page 131:",
"text": "[…] 7. There are 47 occurrences of 47 in the first thousand prime numbers. 8. The atomic number of Silver is 47. 9. It is a Carol number. […]",
"type": "quote"
},
{
"ref": "2019, Dr. Ir. Maarten Looijen, Over getallen gesproken - Talking about numbers, page 70:",
"text": "In 2007 the largest Carol number was found for n = 253987, consisting of 152916 digits, by using the programs MultiSieve and PrimeFormGW.",
"type": "quote"
},
{
"ref": "2021, Elena Deza, Mersenne Numbers And Fermat Numbers, page 136:",
"text": "For ngt;2, the binary representation of the n-th Carol number is n-2 consecutive unities, a single zero in the middle, and n#43;1 more consecutive unities, or to put it algebraically, #92;textstyle#123;CN(n)#61;#92;sum#95;#123;i#61;1,i#92;nen#43;2#125;#123;2n#125;2#123;i-1",
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"glosses": [
"An integer of the form 4ⁿ-2ⁿ⁺¹-1."
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"(mathematics) An integer of the form 4ⁿ-2ⁿ⁺¹-1."
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"word": "Carol number"
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"ref": "2009, The Philosophers' Magazine - Issue 47, page 4:",
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"ref": "2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, page 131:",
"text": "[…] 7. There are 47 occurrences of 47 in the first thousand prime numbers. 8. The atomic number of Silver is 47. 9. It is a Carol number. […]",
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"ref": "2019, Dr. Ir. Maarten Looijen, Over getallen gesproken - Talking about numbers, page 70:",
"text": "In 2007 the largest Carol number was found for n = 253987, consisting of 152916 digits, by using the programs MultiSieve and PrimeFormGW.",
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"ref": "2021, Elena Deza, Mersenne Numbers And Fermat Numbers, page 136:",
"text": "For ngt;2, the binary representation of the n-th Carol number is n-2 consecutive unities, a single zero in the middle, and n#43;1 more consecutive unities, or to put it algebraically, #92;textstyle#123;CN(n)#61;#92;sum#95;#123;i#61;1,i#92;nen#43;2#125;#123;2n#125;2#123;i-1",
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Download raw JSONL data for Carol number meaning in All languages combined (2.0kB)
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-02-03 from the enwiktionary dump dated 2025-01-20 using wiktextract (05fdf6b and 9dbd323). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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