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Product of two prime numbers
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
Semiprime
Natural number
number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures
4
Generalizations of prime ideals and prime rings
mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also
Semiprime_ring
Natural number
preceding 35. 34 is the twelfth semiprime, with four divisors including 1 and itself. Specifically, 34 is the ninth distinct semiprime, it being the sixth of the
34_(number)
Set of large semiprimes
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The
RSA_numbers
Natural number
twenty-seventh distinct semiprime and the second of the form (7.q), where q is a higher prime. the aliquot sum of 91 is 21; itself a semiprime, within an aliquot
91_(number)
Natural number
thirtieth semiprime, and the twenty-sixth distinct semiprime and the eighth of the form (3.q). together with 85 and 86, forms the last semiprime in the 2nd
87_(number)
Natural number
triangular numbers, making it a tetrahedral number. 35 is the 10th discrete semiprime ( 5 × 7 {\displaystyle 5\times 7} ) and the first with 5 as the lowest
35_(number)
Natural number
numbers (5 and 17), and is therefore a semiprime of the form (5.q) where q is prime. specifically, the 24th Semiprime, it being the fourth of the form (5
85_(number)
Natural number
Euler's totient function. 278 is the smallest semiprime number that has an anagram that is also semiprime. The other number is 287. List of highways numbered
278_(number)
Natural number
a semiprime, and a square-free integer. 58 is the sum of the first seven primes. Sloane, Neil; Guy, R. K. (22 August 2010). "A001358: Semiprimes (or
58_(number)
Natural number
a pronic number, a congruent number, a harmonic divisor number, and a semiprime. 6 is also the first Granville number, or S {\displaystyle {\mathcal {S}}}
6
Natural number
and the sixth semiprime and the first odd and fourth discrete semiprime. Its proper divisors are 1, 3, and 5, so it is the first semiprime of the form 3
15_(number)
Decomposition of a number into a product
hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance
Integer_factorization
Concept in algebra
the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal or reduced ideal) is an ideal that is equal to its radical. The
Radical_of_an_ideal
Ideal in a ring which has properties similar to prime elements
ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is prime if it has the following two
Prime_ideal
Natural number
24th triangular number. It is also a second hexagonal number. 303 is a semiprime number. There are 303 compositions of 10 where they cannot be viewed as
300_(number)
Natural number
(sixty-two) is the natural number following 61 and preceding 63. 62 is a semiprime. It is also the number of faces of two of the Archimedean solids, the
62_(number)
Result in ring theory
right annihilators of subsets of R. Goldie's theorem states that the semiprime right Goldie rings are precisely those that have a semisimple Artinian
Goldie's_theorem
Natural number
century AD, under the Gregorian calendar. Twenty-one is the fifth distinct semiprime, and the second of the form 3 × q {\displaystyle 3\times q} where q {\displaystyle
21_(number)
Natural number
distinct semiprime and the 13th of the form (2q); together with 85 and 87, forms the middle semiprime in the 2nd cluster of three consecutive semiprimes; the
86_(number)
Natural number
28th distinct semiprime and the 9th of the form (3.q) where q is a higher prime. the first number in the 3rd triplet of consecutive semiprimes, 93, 94, 95
93_(number)
Natural number
40. 39 is the 12th distinct semiprime and the 4th in the (3.q) family. It is the last member of the third distinct semiprime pair (38,39). 39 is the sum
39_(number)
Natural number
Additionally, 29 represents the sum of the first cluster of consecutive semiprimes with distinct prime factors (14, 15). These two numbers are the only numbers
29_(number)
Natural number
Although it is not a semiprime, the three closest numbers on either side of it are, making it the middle number between twin semiprime-triples, the smallest
216_(number)
Prime number p where p+2 is prime or semiprime
if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen's theorem. The Chen
Chen_prime
Integer having a non-trivial divisor
number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence squares of
Composite_number
Base-6 numeral system
by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the product of the only two consecutive numbers
Senary
Natural number
(twenty-two) is the natural number following 21 and preceding 23. 22 is a semiprime, a Smith number, and an Erdős–Woods number. 22 7 = 3.14 28 … {\displaystyle
22_(number)
Natural number
292. 291 is an odd composite number with two prime factors. 291 is a semiprime number meaning that it has 2 prime factors. 291 can be written as the
291_(number)
Every large even number is either sum of a prime and a semi-prime or two primes
number can be written as the sum of either two primes or a prime and a semiprime (the product of two primes). It is a weakened form of Goldbach's conjecture
Chen's_theorem
Natural number
composite number with 2 prime factors, namely 7 and 41. This makes it a semiprime. 287 is the sum of consecutive primes in three different ways, 89+97+101
287_(number)
Natural number
integer requiring five syllables in English. 77 is: the 22nd discrete semiprime and the first of the (7.q) family, where q is a higher prime. with a prime
77_(number)
Natural number
common factors below it, making 122 a noncototient as well. 122 is a semiprime. φ(122) = φ(σ(122)).[clarification needed] Sloane, N. J. A. (ed.). "Sequence
122_(number)
Number divisible only by 1 and itself
sufficiently large even number can be expressed as the sum of a prime and a semiprime (the product of two primes). Also, any even integer greater than 10 can
Prime_number
Natural number
number following 73 and preceding 75. 74 is: the twenty-first distinct semiprime and the eleventh of the form (2.q), where q is a higher prime. with an
74_(number)
Natural number
number following 93 and preceding 95. 94 is: the twenty-ninth distinct semiprime and the fourteenth of the form (2.q). the ninth composite number in the
94_(number)
Four basic unsolved problems about prime numbers
+ q {\displaystyle 2n=p+q} where p is prime and q is either prime or semiprime. Bordignon, Johnston, and Starichkova, correcting and improving on Yamada
Landau's_problems
Natural number
prime factorization 3 ⋅ 19 {\displaystyle 3\cdot 19} , and is therefore a semiprime. Its proper divisors are 1, 3, and 19, whose sum is 23, so 57 is a deficient
57_(number)
Unsolved problem in cryptography
(mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be
RSA_problem
Numbers obtained by adding the two previous ones
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Fibonacci_sequence
Natural number
is a composite number and the first number which is neither prime nor semiprime. By Mihăilescu's Theorem, it is the only nonzero perfect power that is
8
Natural number
resulted in it being associated in meme culture also with sex. 69 is a semiprime, or a natural number that is the product of exactly two prime numbers
69_(number)
Natural number
number following 154 and preceding 156. 155 is: a composite number a semiprime. a deficient number, since 1+5+31=37<155. odious, since its binary expansion
155_(number)
Class of prime numbers
also in places to treat semiprimes in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits
Emirp
Composite number that passes Fermat's probable primality test
Except for 561 = 3⋅11⋅17, only semiprimes can occur in the above sequence. Not all semiprimes less than 561 occur; a semiprime pq (p ≤ q) less than 561 occurs
Fermat_pseudoprime
Natural number
following 248 and preceding 250. Additionally, 249 is: a Blum integer. a semiprime. palindromic in base 82 (3382). a Harshad number in bases 3, 83, 84, 124
249_(number)
Number equal to the sum of its proper divisors
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Perfect_number
Natural number
{\displaystyle 177=2^{7}+7^{2}.} The fifty-seventh semiprime is 177 (after the square of 13), and it is the 51st semiprime with distinct prime factors. The magic
177_(number)
Natural number
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
161_(number)
Integer that divides another integer
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Divisor
Algebraic structure
right annihilators of subsets of R. Goldie's theorem states that the semiprime right Goldie rings are precisely those that have a semisimple Artinian
Noncommutative_ring
Mathematical function
assume N = pq is a semiprime then the following process can be used to compute an eta-quotient basis of Mk(Γ0(N)). Fix a semiprime N = pq which is coprime
Dedekind_eta_function
Logic puzzle
the fact that P would immediately know X and Y if their product were a semiprime, it can be deduced that the sum x+y cannot be even, since every even number
Sum_and_Product_Puzzle
Process of converting plaintext to ciphertext
prime numbers to create a semiprime number for its public key. Decoding this key without its private key requires this semiprime number to be factored, which
Encryption
Submodule of a mathematical ring
domain for commutative rings. Radical ideal or semiprime ideal: A proper ideal I is called radical or semiprime if for any a in R {\displaystyle R} , if an
Ideal_(ring_theory)
Natural number
the 34th prime number. It is a twin prime with 137. Because 141 is a semiprime, 139 is a Chen prime. 139 is the smallest prime before a prime gap of
139_(number)
Natural number
cyclic number formed from the reciprocal of the number three. 133 is a semiprime: a product of two prime numbers, namely 7 and 19. Since those prime factors
133_(number)
Natural number
sixty-five) is the natural number following 364 and preceding 366. 365 is a semiprime centered square number. It is also the fifth 38-gonal number. It is the
365_(number)
Iterative algorithm on numbers
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Kaprekar's_routine
Natural number
Kummer number. However, the Kummer numbers are not all prime, and as a semiprime (the product of two smaller prime numbers 11 × 19), 209 is the first example
209_(number)
Natural number
fourteen) is the natural number following 213 and preceding 215. 214 is a semiprime, and a 37-gonal number (37-gonal number). 214!! − 1 is a 205-digit prime
214_(number)
Natural number
< 254.[better source needed] It is a semiprime number. Moreover, in American English, its name has a semiprime number of syllables. It is a square-free
254_(number)
Natural number
(95,25, 6, 1). 95 is the last member in the third triplet of distinct semiprimes 93, 94, and 95. 95 is the smallest composite Thabit number. 95 is the
95_(number)
Number theory conjecture about odd integers
than 5 can be represented as the sum of an odd prime number and an even semiprime. The conjecture was first proposed by Émile Lemoine in 1895, but was erroneously
Lemoine's_conjecture
Cryptographic solution
the plaintext. Ron Rivest estimated in 1977 that factoring a 125-digit semiprime would require 40 quadrillion years, using the best algorithm known and
The Magic Words are Squeamish Ossifrage
The_Magic_Words_are_Squeamish_Ossifrage
Accomplishments in factoring large integers
its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers that have no small factors). The first enormous
Integer_factorization_records
Conjecture about prime gaps
either prime or a square-free number with at most 2 prime factors (a semiprime). Let π n ( x ) {\displaystyle \pi _{n}(x)} for even n be the number of
Polignac's_conjecture
nilpotent ideal. semiprime 1. A semiprime ring is a ring where the only nilpotent ideal is the trivial ideal {0}. A commutative ring is semiprime if and only
Glossary_of_ring_theory
Natural number
8^{2}+7^{2}+4^{2}} . 129 is the product of only two primes, 3 and 43, making 129 a semiprime. Since 3 and 43 are both Gaussian primes, this means that 129 is a Blum
129_(number)
Challenge for factoring large semiprimes
and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with
RSA_Factoring_Challenge
Natural number
pieces made by cutting an annulus with 22 cuts. 275 is the smallest non semiprime that follows the equations n>1 and the greatest common denominator of
275_(number)
Integer which is the sum of its positive unitary divisors, not including itself
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Unitary_perfect_number
Integers have unique prime factorizations
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Integer filtered out using a sieve similar to that of Eratosthenes
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Lucky_number
Number without repeated prime factors
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Square-free_integer
Composite number which passes Miller–Rabin primality test
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Strong_pseudoprime
(OEIS: A051131) Chen primes are primes p such that p+2 is either a prime or semiprime. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83
List_of_prime_numbers
Concept in number theory
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Narcissistic_number
Sum of all proper divisors of a natural number
form of Goldbach's conjecture together with the observation that, for a semiprime number pq, the aliquot sum is p + q + 1. The mathematicians Pollack &
Aliquot_sum
Natural number
and real part of the form 3 n − 1 {\displaystyle 3n-1} . Since 913 is a semiprime, 911 is a Chen prime. It is also a centered decagonal number. There are
900_(number)
Numbers with many divisors
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Highly_composite_number
Even integers as sums of two primes
number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). See Chen's theorem for further information
Goldbach's_conjecture
Practice and study of secure communication techniques
The most famous of these are the difficulty of integer factorization of semiprimes and the difficulty of calculating discrete logarithms, both of which are
Cryptography
Natural number, composite number
fourteen in Wiktionary, the free dictionary. 14 is the third distinct semiprime, being the third of the form 2 × q {\displaystyle 2\times q} (where q
14_(number)
Infinite integer series where the next number is the sum of the two preceding it
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Lucas_number
Natural number
two distinct prime numbers 3 and 71, it is a semiprime, the first of a triple of three consecutive semiprimes 213, 214, and 215. Its square, 2132 = 45369
213_(number)
Product of an integer with itself
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Square_number
Number, product of consecutive integers
Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular
Pronic_number
Natural number
3 n − 1 {\displaystyle 3n-1} . Because the next odd number, 133, is a semiprime, 131 is a Chen prime. 131 is an Ulam number. 131 is also a Honaker prime
131_(number)
Prime number of the form that allows fast modular reduction
Frobenius Lucas Perrin Somer–Lucas Strong Carmichael number Almost prime Semiprime Sphenic number Interprime Pernicious Related topics Probable prime Industrial-grade
Solinas_prime
Number in the 5th cell of any row of Pascal's triangle
pentatope number (it needs to check only −1 and 4 = 22), and the largest semiprime which is the predecessor of a pentatope number is 1819. Similarly, the
Pentatope_number
Figurate number
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Triangular_number
Natural number
unlabeled vertices, and 142 partial involutions on five elements. It is a semiprime. It is also palindromic in base 3 (12021). At the United States Merchant
142_(number)
Natural number
natural number following 64 and preceding 66. 65 is the nineteenth distinct semiprime, (5.13); and the third of the form (5.q), where q is a higher prime. 65
65_(number)
Ten raised to an integer power
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Power_of_10
Natural number
fifteen) is the natural number following 214 and preceding 216. 215 is a semiprime. 215 = ( 3 ! ) 3 − 1 {\displaystyle 215=(3!)^{3}-1} . 215 is the coefficient
215_(number)
Sequence of integers
Superior highly composite Superperfect Prime omega functions Almost prime Semiprime Euler's totient function Highly cototient Highly totient Noncototient
Padovan_sequence
Natural number
A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane
167_(number)
Product of prime numbers, plus one
Frobenius Lucas Perrin Somer–Lucas Strong Carmichael number Almost prime Semiprime Sphenic number Interprime Pernicious Related topics Probable prime Industrial-grade
Euclid_number
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