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Fortunate Number
A Fortunate number, named after Reo Fortune, is the smallest integer ''m'' > 1 such that, for a given positive integer ''n'', ''p''''n''# + ''m'' is a prime number, where the primorial ''p''''n''# is the product of the first ''n'' prime numbers. For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3. One would similarly rule out the integers up to 18. Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number. The Fortunate number for ''p''''n''# is always above ''p''''n'' and all its divisors are larger than ''p''''n''. This is because ''p''''n''#, and thus ''p''''n''# + ''m'', is divisible by the prime factors of ''m'' not larger than ''p''''n''. The Fortunate numbers for the first primorials are: : 3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reo Fortune
Reo Franklin Fortune (27 March 1903 – 25 November 1979) was a New Zealand-born social anthropologist. Originally trained as a psychologist, Fortune was a student of some of the major theorists of British and American social anthropology including Alfred Cort Haddon, Bronislaw Malinowski and Alfred Radcliffe-Brown.Thomas, Caroline (2009) "Rediscovering Reo: Reflections on the life and anthropological career of Reo Franklin Fortune," ''Pacific Studies'', vol. 32, nos. 2/3; June–Sept He lived an international life, holding various academic and government positions: in China, at Lingnan University from 1937 to 1939; in Toledo, Ohio, USA from 1940 to 1941; at the University of Toronto, from 1941 to 1943; in Burma, as government anthropologist, from 1946 to 1947; and finally, at Cambridge University in the United Kingdom from 1947 to 1971, as lecturer in social anthropology specialising in Melanesian languages, Melanesian language and culture.Gray, Geoffrey "Being honest to my ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
37 (number)
37 (thirty-seven) is the natural number following 36 and preceding 38. In mathematics 37 is the 12th prime number and the third unique prime in decimal. 37 is the first irregular prime, and the third isolated prime without a twin prime. It is also the third cuban prime, the fourth emirp, and the fifth lucky prime. *37 is the third star number and the fourth centered hexagonal number. *The sum of the squares of the first 37 primes is divisible by 37. *Every positive integer is the sum of at most 37 fifth powers (see Waring's problem). *37 appears in the Padovan sequence, preceded by the terms 16, 21, and 28 (it is the sum of the first two of these). *Since the greatest prime factor of 372 + 1 = 1370 is 137, which is substantially more than 37 twice, 37 is a Størmer number. In base-ten, 37 is a permutable prime with 73, which is the 21st prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime. In moonshine theory, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Pages
The PrimePages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin. The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" lists for primes of various forms. , the 5,000th prime has around 412,000 digits.. Retrieved on 2018-02-12. The PrimePages has articles on primes and primality testing. It includes "The Prime Glossary" with articles on hundreds of glosses related to primes, and "Prime Curios!" with thousands of curios about specific numbers. The database started as a list of titanic primes (primes with at least 1000 decimal digits) by Samuel Yates. In subsequent years, the whole top-5,000 has consisted of gigantic primes (primes with at least 10,000 decimal digits). Primes of special forms are kept on the current lists if they are titanic and in the top-20 or top-5 for their form. See also *List of prime numbers This is a list of articles about pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
109 (number)
109 (one hundred ndnine) is the natural number following 108 and preceding 110. In mathematics 109 is the 29th prime number. As 29 is itself prime, 109 is a super-prime. The previous prime is 107, making them both twin primes. 109 is a centered triangular number. The decimal expansion of 1/109 can be computed using the alternating series, with F(n) the n^ Fibonacci number: ::\frac=\sum_^\infty\times (-1)^=0.00917431\dots The decimal expansion of 1/109 has 108 digits, making 109 a full reptend prime in decimal. The last six digits of the 108-digit cycle are 853211, the first six Fibonacci numbers in descending order. There are exactly 109 different families of subsets of a three-element set whose union includes all three elements, 109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements, and 109 squares on an infinite chessboard that can be reached by a knight within three moves. See also *109 (other) 109 ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
59 (number)
59 (fifty-nine) is the natural number following 58 and preceding 60. In mathematics Fifty-nine is the 17th prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form . Since is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime. It is also a highly cototient number. There are 59 stellations of the regular icosahedron, inclusive of the icosahedron. 59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13 # + 1 = 2 × 3 × 5 × 7 × 11 × 13 + 1 = 59 × 509 = 30031. 59 is the highest integer a single symbol may represent in the Sexagesimal system. As 17 is prime, 59 is a super-prime. The number 59 takes 3 iterations of the "reverse and add" process to form the palindrome 1111. All smaller integers (1 through 58) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
107 (number)
107 (one hundred ndseven) is the natural number following 106 and preceding 108. In mathematics 107 is the 28th prime number. The next prime is 109, with which it comprises a twin prime, making 107 a Chen prime. Plugged into the expression 2^p - 1, 107 yields 162259276829213363391578010288127, a Mersenne prime. 107 is itself a safe prime. It is the fourth Busy beaver number, the maximum number of steps that any Turing machine with 2 symbols and 4 states can make before eventually halting. It is the number of triangle-free graphs on 7 vertices. It is the ninth emirp, because reversing it's digits gives another prime number (701) In other fields As "one hundred ''and'' seven", it is the smallest positive integer requiring six syllables in English (without the "and" it only has five syllables and seventy-seven is a smaller 5-syllable number). 107 is also: * The atomic number of bohrium. * The emergency telephone number in Argentina and Cape Town. * The telephone of the poli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
47 (number)
47 (forty-seven) is the natural number following 46 (number), 46 and preceding 48 (number), 48. It is a prime number. In mathematics Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime (moonshine theory), supersingular prime, the fourth isolated prime, and the sixth Lucas prime. Forty-seven is a highly cototient number. It is an Eisenstein prime with no imaginary part and real part of the form . It is a Lucas number. It is also a Keith number because its digits appear as successive terms earlier in the series of Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... It is the number of Tree (graph theory), trees on 9 unlabeled nodes. Forty-seven is a strictly non-palindromic number. Its representation in binary being 101111, 47 is a prime Thabit number, and as such is related to the pair of amicable numbers . In science * 47 is the atomic number of silver. Astronomy * The 47-year cycle of Mars: after 47 years – 22 Synodic period, synodic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 (number)
71 (seventy-one) is the natural number following 70 (number), 70 and preceding 72 (number), 72. __TOC__ In mathematics 71 is: *the 20th prime number. The next is 73 (number), 73, with which it composes a twin prime. *a permutable prime and emirp with 17 (number), 17. *is the largest number which occurs as a prime factor of an order of a sporadic simple group. *the sum of three consecutive primes: 19 (number), 19, 23 (number), 23 and 29 (number), 29. *a centered heptagonal number. *an Eisenstein prime with no imaginary part and real part of the form 3''n'' – 1. *a Pillai prime, since 9! + 1 is divisible by 71 but 71 is not one more than a multiple of 9. *the largest (15th) Supersingular prime (moonshine theory), supersingular prime, which is also a Chen prime. *part of the last known pair (71, 7) of Brown numbers, since 712 = 7! + 1. *the twenty-third term of the Euclid–Mullin sequence, as it is the least prime factor of one more than th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
67 (number)
67 (sixty-seven) is the natural number following 66 (number), 66 and preceding 68 (number), 68. It is an Parity (mathematics), odd number. In mathematics 67 is: *the 19th prime number (the next is 71 (number), 71). * a Chen prime. *an irregular prime. *a lucky prime. *the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). *a Heegner number. *a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. *palindromic in quinary (2325) and senary (1516). *a super-prime. (19 is prime) *an isolated prime. (65 and 69 aren't prime) In science *The atomic number of holmium, a lanthanide. Astronomy *Messier object Messier 67, M67, a visual magnitude, magnitude 7.5 open cluster in the constellation Cancer (constellation), Cancer. *The New General Catalogue object NGC 67, an elliptical galaxy in the constellation Andromeda (constellation), Andromeda. In music * "Car 67", a song by the band Driver 67 * Chicago (band), Chicago's song "Questions 67 and 6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
61 (number)
61 (sixty-one) is the natural number following 60 and preceding 62. In mathematics 61 is: *the 18th prime number. *a twin prime with 59. *a cuban prime of the form ''p'' = , where ''x'' = ''y'' + 1. *the smallest ''proper prime'', a prime ''p'' which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repeating sequence with length ''p'' − 1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, times). *the exponent of the 9th Mersenne prime. (261 − 1 = ) *the sum of two squares, 52 + 62. *a centered square number. *a centered hexagonal number. *a centered decagonal number. *the sixth Euler zigzag number (or Up/down number). *a unique prime in base 14, since no other prime has a 6-digit period in base 14. *a Pillai prime since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8. *a Keith number, because it recurs in a Fibonacci-like sequence started from i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19 (number)
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. Mathematics 19 is the eighth prime number, and forms a sexy prime with 13, a twin prime with 17, and a cousin prime with 23. It is the third full reptend prime, the fifth central trinomial coefficient, and the seventh Mersenne prime exponent. It is also the second Keith number, and more specifically the first Keith prime. * 19 is the maximum number of fourth powers needed to sum up to any natural number, and in the context of Waring's problem, 19 is the fourth value of g(k). * The sum of the squares of the first 19 primes is divisible by 19. *19 is the sixth Heegner number. 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total. * 19 is the third centered triangular number as well as the third centered hexagonal number. : The 19th triangular number is 190, equivalently the sum of the first 19 non-zero integers, that is al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
