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Questions tagged [semiprimes]

A semiprime is a natural number that is the product of two prime numbers. This tag is intended for questions about, related to, or involving semiprime numbers.

A semiprime, also called a 2-almost prime, biprime or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few are 4, 6, 9, 10, 14, 15, 21, 22, ... (OEIS A001358).

Semiprimes are highly useful in the area of cryptography and number theory, most notably in public key cryptography, where they are used by RSA. It relies on the fact that finding two large primes and multiplying them together (resulting in a semiprime) is computationally simple, whereas finding the original factors appears to be difficult.

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Digital root of twin prime semiprimes

It appears that the product of any pair of twin primes (excluding the first pair 3 and 5) yields a semi prime whose digital root is equal to $8$. Example: $$ 17 \cdot 19 = 323 $$ The digital root of $323$ is $8$. I've tested the first twenty and a…
Tony
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relative size of most factors of semiprimes, close?

when chatting about RSA a cohort just asserted something like "most prime factors of semiprimes are roughly the same size" measured in bits. ie "bits" is the number of digits in the base2 representations of the two primes. am skeptical myself.…
vzn
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Can you derive a formula for the semiprime counting function from the prime number theorem?

E.g., there are $4$ semiprimes less than or equal to $10$ $(4, 6, 9, 10)$ or $2$ squarefree semiprimes ($6$ and $10$). It's ok if it's off for small numbers but gets more accurate as $n \to \infty$.
user155234
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Check if a Number is Semiprime

I would like to know if there's a quick way to check if a number is semiprime. By far all the links I have seen only tell either how to generate a semiprime or count the number of semiprimes or to factorize it... But I just want to check whether it…
Kartik Khare
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What is an upper bound for number of semiprimes less than $n$?

A semiprime is a number that is the product of two prime numbers. What is an upper bound for the number of numbers of the form $pq$ less than $n$? $p,q$ are prime numbers smaller than $n$.
ttt
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Conjecture: Every Non-Zero Integer as the Difference of a Semiprime and a Prime

I would like to propose the following conjecture and seek insights or references related to it: Conjecture: Every non-zero integer $n$ can be expressed as the difference of a semiprime $q$ and a prime $p$, that is, $$n=q−p,$$ where: q is a semiprime…
Akira Sukigi
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Problems about consecutive semiprimes

I was playing around with semi-prime numbers and I made two conjectures, which are: Given any integer $a$, at least one of $a,(a+1),(a+2)$ or $(a+3)$ is not semi-prime. There are infinitely many integers $a$, such that $a,(a+1)$ and $(a+2)$ are…
Obinna Okechukwu
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Extending the zeta function to semiprimes, etc.

The Riemann Zeta function is defined for $s > 1$ as \begin{align} &\prod _{n=1}^{\infty}\dfrac{1}{1 -\ p_{n}^{\ \ -s}}\\ \end{align} It is possible to extend the zeta function to semiprimes with \begin{align} &\prod _{n=1}^{\infty}\dfrac{1}{1 -\…
martin
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Are there infinitely many primes of the form $y = 2p_1p_2 + 1$?

I came up with this (I admit I'm probably not the first one to have this thought but I haven't been able to find anyone else with the same question) while reading about semiprimes. Clearly $y$ is always odd which suggests to me that it could also be…
Daan Koning
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Semiprime numbers which, along with their prime factors, generate many semiprimes by concatenation

There's something quite interesting about the number $1191$: this number is a semiprime ($1191= 3 \cdot 397$), the concatenation of its prime factors in any order are semiprimes ($3397$ and $3973$ are semiprimes), but not just that, if you…
Bernard L
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Semiprime asymptotic step function

Since $$\pi_{(2)}(x)=\sum_{i=1}^{\pi(x^{1/2})}\left(\pi\left(\dfrac{x}{\text{p}_i}\right)-i+1\right),$$ where $\pi_{(2)}(x)$ denotes the semiprimes and $\text{P}_i$ is the $i$th prime, an asymptotic of the semiprimes may be given…
martin
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Is $\gcd(n, \lfloor\sqrt{n}\rfloor!)$ a solution to the factoring problem?

The factoring problem: Factor $n=pq$ given only $n$ where $p$ and $q$ are primes and $0
zerosofthezeta
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reciprocals of squarefree k-almost primes

First of all, I'm a novice in math and English is not my native language, so I apologize in advance for any incorrect wording, etc. Definitions and specific example Let's define the set $A_4 = \{2,3,5,7\}$, with the first 4 prime numbers. And…
Pim Dumans
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Density of semiprimes on short intervals

Perhaps this is a trivial question, but I'm not an expert. Let $$Q(m) = \bigl| \{ n : m\leq n \leq m + \log(m) \mbox{ and } n = p \cdot q\text{, where }p,q\text{ are prime} \} \bigr|$$ i.e., $Q(m)$ is the size of the set containing the numbers…
Vor
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$28222149$, a semiprime with amazing properties

The semiprime $28222149$ is a semiprime $S=A*B$ (with $A=3$ and $B=9407383$) such that -$A.B$ -$B.A$ -$S.A$ -$S.B$ -$A.S$ -$S.A.B$ -$S.B.A$ -$A.S.B$ -$A.B.S$ -$B.S.A$ -$B.A.S$ are all semiprime. (Dots here means concatenation.) It would be a…
Nyaku T
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