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Additive Prime
This is a list of articles about prime numbers. A prime number (or ''prime'') is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. 1 is neither prime nor composite. The first 1000 prime numbers The following table lists the first 1000 primes, with 20 columns of consecutive primes in each of the 50 rows. . The Goldbach conjecture verification project reports that it has computed all primes smaller than 4×10. That means 95,676,260,903,887,607 primes (nearly 10), but they were not stored. There are known formulae to evaluate the prime-counting function (the number of primes smaller than a given value) faster than computing the primes. This has be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorization, factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
53 (number)
53 (fifty-three) is the natural number following 52 (number), 52 and preceding 54 (number), 54. It is the 16th prime number. In mathematics Fifty-three is the 16th prime number. It is the second balanced prime, and fifth isolated prime. 53 is a sexy prime with 47 (number), 47 and 59 (number), 59. It is the eighth Sophie Germain prime, and the ninth Eisenstein prime. The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers. 53 cannot be expressed as the sum of any integer and its decimal digits, making 53 the ninth self number in decimal. 53 is the smallest prime number that does not divide the order of any sporadic group, inclusive of the six Pariah group, pariahs; it is also the first prime number that is not a member of Bhargava's prime-universality criterion theorem (followed by the next prime number 59 (number), 59), an integer-matrix quadratic form that represents all prime numbers when it represents the sequence of s ... [...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 the tenth super-prime. The previous prime is 107, making them both twin primes. 109 is a centered triangular number. 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. *109 squares on an infinite chessboard that can be reached by a knight within three moves. There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings. 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 10 ... [...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 its digits gives another prime number (701) In other fields 107 is also: * The emergency telephone number in Argentina and Cape Town. * The telephone of the police in Hungary. In sports * The 107% rule, a Formula One Sporting Regulation in operation from 1996 to 2002 and 2011 onward. * The number 107 is also associated with the Timbers Army supporters group of the Portland Timbers socc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
103 (number)
103 (one hundred ndthree) is the natural number following 102 and preceding 104. In mathematics 103 is a prime number, and the largest prime factor of 6!+1=721=7\cdot 103. The previous prime is 101. This makes 103 a twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' .... It is the fifth irregular prime, because it divides the numerator of the Bernoulli number B_=-\frac=-\frac. The equation 64^3+94^3=103^3+1 makes 103 part of a "Fermat near miss". There are 103 different connected series-parallel partial orders on exactly six unlabeled elements. 103 is conjectured to be the smallest number for which repeatedly reversing the digits of its ternary representation, and adding the number to its reversal, does not eventually reach a ternary palindrome. References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
101 (number)
101 (one hundred ndone) is the umberfollowing 100 and preceding 102. It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one". As an ordinal number, 101st (one hundred ndfirst), rather than 101th, is the correct form. 101 is a prime number and the smallest integer above 100. It is also a palindromic number, and hence, a palindromic prime. In mathematics 101 is an alternating factorial, sexy prime and 101 is also the smallest number that can be expressed as the sum of three distinct nonzero squares in more than two ways: 9^2+4^2+2^2, 8^2+6^2+1^2 or 7^2+6^2+4^2 (see image). For a 3-digit number in decimal, this number has a relatively simple divisibility test. The candidate number is split into groups of four, starting with the rightmost four, and added up to produce a 4-digit number. If this 4-digit number is of the form 1000a+100b+10a+b (where and are integers from 0 to 9), such as 3232 or 9797 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
97 (number)
97 (ninety-seven) is the natural number following 96 (number), 96 and preceding 98 (number), 98. It is a prime number and the only prime in the nineties. In mathematics 97 is: * the 25th prime number (the largest two-digit prime number in Base 10, base 10), following 89 (number), 89 and preceding 101 (number), 101. * a Proth prime and a Pierpont prime as it is 3 × 25 + 1. * the eleventh member of the Mian–Chowla sequence. * a self number in base 10, since there is no integer that added to its own digits, adds up to 97. * the smallest odd prime that is not a cluster prime. * the highest two-digit number where the sum of its digits is a square. * the number of primes less than 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all happy primes. However, 9000007 (read as ''nine million seven'') is composite number, composite and has the factorization 277 (number), 277 × 32491. * an emirp with 79 (number), 79. * an isolated p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
89 (number)
89 (eighty-nine) is the natural number following 88 and preceding 90. In mathematics 89 is: * the 24th prime number, following 83 and preceding 97. * a Chen prime. * a Pythagorean prime. * the smallest Sophie Germain prime to start a Cunningham chain of the first kind of six terms, . * an Eisenstein prime with no imaginary part and real part of the form . * The 11th Fibonacci number and thus a Fibonacci prime as well. The first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity ::\frac=\sum_^\infty=0.011235955\dots\ . * a Markov number, appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers. ''M''89 is the 10th Mersenne prime. Although 89 is not a Lychrel number in base 10, it is unusual that it takes 24 iterations of the reverse and add process to reach a palindrome. Among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
83 (number)
83 (eighty-three) is the natural number following 82 and preceding 84. In mathematics 83 is: * the sum of three consecutive primes (23 + 29 + 31). * the sum of five consecutive primes (11 + 13 + 17 + 19 + 23). * the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89. * a Sophie Germain prime. * a safe prime. * a Chen prime. * an Eisenstein prime with no imaginary part and real part of the form 3''n'' − 1. * a highly cototient number. * the number of primes that are right-truncatable. * a super-prime, because 23 is prime. In other fields * The eighth letter of the alphabet is H and the third letter is C, thus 83 stands for "Heil Christ," a greeting used by organizations that consider themselves also to be Christian. * An emoticon An emoticon (, , rarely , ), short for emotion icon, is a pictorial representation of a facial expression using Character (symbol), characters—usually punctuation marks, numbers and Alphabet, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
79 (number)
79 (seventy-nine) is the natural number following 78 (number), 78 and preceding 80 (number), 80. In mathematics 79 is: * An even and odd numbers, odd number. * The smallest number that can not be represented as a sum of fewer than 19 fourth powers. * The 22nd prime number (between and ) * An isolated prime without a twin prime, as 77 and 81 are composite. * The smallest prime number ''p'' for which the real quadratic field Q[] has Ideal class group, class number greater than 1 (namely 3). * A cousin prime with 83. * An emirp in base 10, because the reverse of 79, 97 (number), 97, is also a prime. * A Fortunate prime. * A circular prime. * A prime number that is also a Gaussian prime (since it is of the form ). * A happy prime. * A Higgs prime. * A lucky prime. * A permutable prime, with 97 (number), ninety-seven. * A Pillai prime, because 23Factorial, ! + 1 is divisible by 79, but 79 is not one more than a Multiple (mathematics), multiple of 23 (number), 23. * A regular prime. * A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
73 (number)
73 (seventy-three) is the natural number following 72 (number), 72 and preceding 74 (number), 74. In English, it is the smallest natural number with twelve letters in its spelled out name. It is the 21st prime number and the fourth star number. It is also the eighth twin prime, with 71 (number), 71. In mathematics 73 is the 21st prime number, and emirp with 37 (number), 37, the 12th prime number. It is also the eighth twin prime, with 71 (number), 71. It is the largest minimal Primitive root modulo n, primitive root in the first 100,000 primes; in other words, if is one of the first one hundred thousand primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., 73 is a primitive root modulo . 73 is also the smallest factor of the first Composite number, composite generalized Fermat number in decimal: 10^+1=10,001=73\times 137, and the smallest prime Modular arithmetic#Congruence, congruent to 1 modulo 24 (number), 24, as well as the only prime repunit in octal (1118). It is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 (number)
71 (seventy-one) is the natural number following 70 and preceding 72. __TOC__ In mathematics 71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. 71 is a centered heptagonal number. It is a regular prime, a Ramanujan prime, a Higgs prime, and a good prime. It is a Pillai prime, since 9!+1 is divisible by 71, but 71 is not one more than a multiple of 9. It is part of the last known pair (71, 7) of Brown numbers, since 71^=7!+1. 71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner number In number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from int ...s). 71 is the largest number which occurs as a prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
