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Blum Integer
In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/cambridge1997.pdf That is, ''p'' and ''q'' must be of the form , for some integer ''t''. Integers of this form are referred to as Blum primes. Goldwasser, S. and Bellare, M.br>"Lecture Notes on Cryptography". Summer course on cryptography, MIT, 1996-2001 This means that the factors of a Blum integer are Gaussian primes with no imaginary part. The first few Blum integers are : 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, ... The integers were named for computer scientist Manuel Blum. Properties Given a Blum integer, ''Q''''n'' the set of all quadratic residues modulo ''n'' and coprime to ''n'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
161 (number)
161 (one hundred ndsixty-one) is the natural number following 160 and preceding 162. In mathematics * 161 is the sum of five consecutive prime numbers: 23, 29, 31, 37, and 41. * 161 is a hexagonal pyramidal number. * 161 is a semiprime. Since its prime factors 7 and 23 are both Gaussian primes, 161 is a Blum integer. * 161 is a palindromic number. * is a commonly used rational approximation of the square root of 5 and is the closest fraction with denominator 88'' (''88'' being code for ''Heil Hitler'' among neo-nazis Neo-Nazism comprises the post–World War II militant, social, and political movements that seek to revive and reinstate Nazi ideology. Neo-Nazis employ their ideology to promote hatred and racial supremacy (often white supremacy), to att ..., as H=8) External links Number Facts and Trivia: 161The Number 161 References {{DEFAULTSORT:161 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
341 (number)
341 (three hundred ndforty-one) is the natural number following 340 and preceding 342. In mathematics * 341 is the sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61). * 341 is an octagonal number and a centered cube number. * 341 is a super-Poulet number. * 341 is the smallest Fermat pseudoprime; it is the ''least'' ''composite'' ''odd'' modulus ''m'' greater than the base ''b'', that satisfies the ''Fermat'' property "''bm''−1 − 1 is divisible by ''m''", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108. * 341 is a palindrome in base 2 (1010101012), 4 (111114), 8 (5258), 17 (13117) and 30 (BB30). * 341 is repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ... in base 4 (111114) and 30 (BB30). References {{Integers, 3 Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
329 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = 11 & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
309 (number)
309 or three hundred nine is the natural number following 308 and preceding 310. In mathematics * 309 is an odd composite number. * 309 is composed of two distinct prime numbers A prime number (or a prime) is a natural number greater than 1 that is not a 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 ... multiplied (103 and 3). * 309 is a Blum integer. * 309 is a centered icosahedral number. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
301 (number)
301 is the natural number following 300 and preceding 302. In mathematics *301 is an odd composite number with two prime factors. *301 is a Stirling number of the second kind represented by meaning that it is the number of ways to organize 7 objects into 3 non-empty sets. *301 is the sum of consecutive primes 97, 101, and 103. *301 is a happy number, meaning that infinitely taking the sum of the squares of the digits will eventually result in 1. *301 is a lazy caterer number meaning that it is the maximum number of pieces made by cutting a circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ... with 24 cuts. References {{Integers, 3 Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
253 (number)
253 (two hundred ndfifty-three) is the natural number following 252 and preceding 254. In mathematics 253 is: *a semiprime since it is the product of 2 primes. *a brilliant number, meaning that its prime factors have the same amount of digits *the 22nd triangular number. *a star number. *a centered heptagonal number A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by .... *a centered nonagonal number. *a Blum integer. *a member of the 13-aliquot tree. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
249 (number)
249 (two hundred ndforty-nine) is the natural number following 248 and preceding 250. Additionally, 249 is: *a Blum integer. *a semiprime. *palindromic in base 82 (3382). *a Harshad number In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ... in bases 3, 83, 84, 124, 167 and 247. *the aliquot sum of any of these numbers: 375, 531, 1687, 4351, 7807, 12127, 14647 and 15151. *part of the 3-aliquot tree. The aliquot sequence starting at 288 is: 288, 531, 249, 87, 33, 15, 9, 4, 3, 1, 0. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
237 (number)
237 (two hundred ndthirty-seven) is the natural number following 236 and preceding 238. 237 is a lucky number In number theory, a lucky number is a natural number in a set which is generated by a certain " sieve". This sieve is similar to the sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the rema ..., and one of the numbers in Aronson's sequence. The 237th square pyramidal number, 4465475, is also a sum of two smaller square pyramidal numbers. There are only four smaller numbers (55, 70, 147, and 226) with the same property. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
217 (number)
217 (two hundred ndseventeen) is the natural number following 216 and preceding 218. In mathematics 217 is a centered hexagonal number, a 12-gonal number, a centered 36-gonal number, a Fermat pseudoprime to base 5, and a Blum integer. It is both the sum of two positive cubes and the difference of two positive consecutive cubes in exactly one way: 217 = 6^3 + 1^3 = 9^3 - 8^3. When written in binary, it is a non-repetitive Kaprekar number. OEIS It is also the sum of all the divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one ...
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213 (number)
213 (two hundred ndthirteen) is the number following 212 and preceding 214. In mathematics 213 and the other permutations of its digits are the only three-digit number whose digit sums and digit products are equal. It is a member of the quickly-growing Levine sequence, constructed from a triangle of numbers in which each row counts the copies of each value in the row below it. As the product of the two distinct prime numbers 3 and 71, it is a semiprime In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime n ..., the first of a triple of three consecutive semiprimes 213, 214, and 215. Its square, 2132 = 45369, is one of only 15 known squares that can be represented as a sum of distinct factorials. See also * 213 (other) References Integers {{Num-stub ca:Nombre 210#No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
