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In number theory, a Thabit number, Thâbit ibn Kurrah number, or 321 number is an integer of the form for a non-negative integer ''n''. The first few Thabit numbers are: :2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ... The 9th Century Iraqi Muslim mathematician, physician, astronomer and translator Thābit ibn Qurra is credited as the first to study these numbers and their relation to amicable numbers. == Properties == The binary representation of the Thabit number 3·2''n''−1 is ''n''+2 digits long, consisting of "10" followed by ''n'' 1s. The first few Thabit numbers that are prime (also known as 321 primes): :2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, ... , there are 62 known prime Thabit numbers. Their ''n'' values are :〔()〕〔()〕〔http://primes.utm.edu/primes/lists/short.txt〕 :0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515, 11484018, 11731850, 11895718 The primes for ''n''≥234760 were found by the distributed computing project 321 search.〔()〕 The largest of these, 3·211895718−1, has 3580969 digits and was found in June 2015. In 2008, Primegrid took over the search for Thabit primes.〔http://primes.utm.edu/bios/page.php?id=479〕 It is still searching and has already found all Thabit primes with n ≥ 4235414.〔http://primes.utm.edu/primes/lists/short.txt〕 It is also searching for primes of the form 3·2''n''+1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thabit number」の詳細全文を読む スポンサード リンク
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