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In mathematics, a natural number n is a Blum integer if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. 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, ... (sequence in the OEIS)

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rdfs:label	Blumovo číslo (cs) Blum integer (en) Intero di Blum (it) Entier de Blum (fr) 블럼 정수 (ko) ブラム数 (ja) Ціле число Блума (uk) 布卢姆数 (zh)
rdfs:comment	Blumovo číslo je v matematice označení pro takové přirozené číslo , které je poloprvočíslem , přičemž a jsou různá prvočísla, jejichž zbytek po dělení 4 je roven 3. Nejmenšími Blumovými čísly jsou 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, ... a posloupnost má identifikátor A016105 v Online encyklopedii celočíselných posloupností (OEIS). Svá jména získala tato čísla po Manuelu Blumovi, venezuelském informatikovi. (cs) En arithmétique, un entier de Blum est un nombre composé produit de deux nombres premiers distincts congrus à 3 modulo 4. Un entier de Blum est un nombre RSA. Ces nombres sont utilisés dans l'algorithme Blum Blum Shub. Les dix premiers entiers de Blums sont : 21, 33, 57, 69, 77, 93, 129, 133, 141 et 161 (pour les 1 000 premiers, voir la suite de l'OEIS). * Portail de la cryptologie * Arithmétique et théorie des nombres (fr) ブラム数とは、暗号理論の概念で、4を法として3に合同な相異なる2つの素数の積となる整数のことである。 (ja) 정수론에서 어떤 자연수 이 다음 조건을 만족하면 이를 블럼 정수(Blum integer)라고 한다. 1. * 은 소수 와 의 곱이다. 2. * 와 는 모두 4를 법으로 했을 때 3과 합동이다. 즉, 과 는 모두 4로 나뉜다. (ko) 在数学中，如果某自然数n = p × q是半素数，其中p和q是两个不同的素数，且等于3 mod 4，则n是布卢姆数。也就是说，对于某个整数t，p和q必须等于4t + 3。这类整数称作布卢姆素数。因此，布卢姆数的因子是没有虚部的高斯素数。前几个布卢姆数为 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 3,41, 381, 3 413, 417, 437, 453, 469, 473, 489, 497, ...（OEIS數列）布卢姆数取名自计算机科学家曼纽尔·布卢姆。 (zh) In mathematics, a natural number n is a Blum integer if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. 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, ... (sequence in the OEIS) (en) In matematica, più precisamente in teoria dei numeri, un numero naturale n è un intero di Blum se dove p e q sono numeri primi congruenti a 3 in modulo 4 (detti anche primi di Blum), cioè se 4 divide sia p - 3 che q - 3. Per ogni intero di Blum n, -1 ha simbolo di Jacobi modulo n pari a +1, nonostante -1 non sia un residuo quadratico modulo n. (it) У математиці натуральне число n є цілим числом Блума, якщо n = p × q — напівпросте число, для якого p і q є різними простими числами, такими що дають остачу 3 при діленні на 4. Тобто, p і q повинні мати вигляд 4t + 3 для деякого цілого t. (uk)
dcterms:subject	Integer sequences
Wikipage page ID	2218352 (xsd:integer)
Wikipage revision ID	1117456473 (xsd:integer)
Link from a Wikipage to another Wikipage	Number field sieve Jacobi symbol 129 (number) 133 (number) 141 (number) 161 (number) Mathematics Quadratic residue 177 (number) Gaussian integer Modular arithmetic 57 (number) 69 (number) 77 (number) 93 (number) 21 (number) 33 (number) Integer sequences Prime number Manuel Blum Natural number RSA (algorithm) Semiprime MPQS
sameAs	Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer Blum integer
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:I_sup dbt:OEIS dbt:Reflist dbt:Classes_of_natural_numbers
has abstract	Blumovo číslo je v matematice označení pro takové přirozené číslo , které je poloprvočíslem , přičemž a jsou různá prvočísla, jejichž zbytek po dělení 4 je roven 3. Nejmenšími Blumovými čísly jsou 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, ... a posloupnost má identifikátor A016105 v Online encyklopedii celočíselných posloupností (OEIS). Svá jména získala tato čísla po Manuelu Blumovi, venezuelském informatikovi. (cs) In mathematics, a natural number n is a Blum integer if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. 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, ... (sequence in the OEIS) The integers were named for computer scientist Manuel Blum. (en) En arithmétique, un entier de Blum est un nombre composé produit de deux nombres premiers distincts congrus à 3 modulo 4. Un entier de Blum est un nombre RSA. Ces nombres sont utilisés dans l'algorithme Blum Blum Shub. Les dix premiers entiers de Blums sont : 21, 33, 57, 69, 77, 93, 129, 133, 141 et 161 (pour les 1 000 premiers, voir la suite de l'OEIS). * Portail de la cryptologie * Arithmétique et théorie des nombres (fr) ブラム数とは、暗号理論の概念で、4を法として3に合同な相異なる2つの素数の積となる整数のことである。 (ja) 정수론에서 어떤 자연수 이 다음 조건을 만족하면 이를 블럼 정수(Blum integer)라고 한다. 1. * 은 소수 와 의 곱이다. 2. * 와 는 모두 4를 법으로 했을 때 3과 합동이다. 즉, 과 는 모두 4로 나뉜다. (ko) In matematica, più precisamente in teoria dei numeri, un numero naturale n è un intero di Blum se dove p e q sono numeri primi congruenti a 3 in modulo 4 (detti anche primi di Blum), cioè se 4 divide sia p - 3 che q - 3. Per ogni intero di Blum n, -1 ha simbolo di Jacobi modulo n pari a +1, nonostante -1 non sia un residuo quadratico modulo n. Prima che i moderni algoritmi di fattorizzazione, come MPQS e NFS, fossero sviluppati, si pensava che fosse utile scegliere interi di Blum per il modulo di RSA. Questo non è più considerato una precauzione utile, poiché MPQS e NFS riescono a fattorizzare interi di Blum con la stessa efficienza di numeri prodotti da primi scelti a caso. (it) У математиці натуральне число n є цілим числом Блума, якщо n = p × q — напівпросте число, для якого p і q є різними простими числами, такими що дають остачу 3 при діленні на 4. Тобто, p і q повинні мати вигляд 4t + 3 для деякого цілого t. Перші кілька цілих чисел Блума — це 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, … (послідовність з Онлайн енциклопедії послідовностей цілих чисел, OEIS). Ці числа названі так на честь Мануеля Блума, вченого відомого досягненнями в галузі теоретичної інформатики. (uk) 在数学中，如果某自然数n = p × q是半素数，其中p和q是两个不同的素数，且等于3 mod 4，则n是布卢姆数。也就是说，对于某个整数t，p和q必须等于4t + 3。这类整数称作布卢姆素数。因此，布卢姆数的因子是没有虚部的高斯素数。前几个布卢姆数为 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 3,41, 381, 3 413, 417, 437, 453, 469, 473, 489, 497, ...（OEIS數列）布卢姆数取名自计算机科学家曼纽尔·布卢姆。 (zh)
gold:hypernym	Integer
prov:wasDerivedFrom	wikipedia-en:Blum_integer?oldid=1117456473&ns=0
page length (characters) of wiki page	3432 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Blum_integer
is Link from a Wikipage to another Wikipage of	217 (number) List of integer sequences 129 (number) 133 (number) 141 (number) 161 (number) Zero-knowledge proof 500 (number) 57 (number) 69 (number) 700 (number) 77 (number) 800 (number) 93 (number) 21 (number) 600 (number) 249 (number)

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