Questions tagged [prime-numbers]

Questions on testing and computing prime numbers.

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efficient code to search for formulas for calculating primes

I had an idea for calculating primes using smaller primes given the following: p1=(p2-p3/p4)+(p5-p6/p7) where p1>p5>p2 and p2>p3>p4 and p5>p6>p7 and p1 through p7 are all prime ...
• 445
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Strange behavior of 'SquareFreeQ'

What is the cause of this strange behavior of SquareFreeQ while PrimePowerQ works correctly: ...
• 2,862
1k views

Making the number 12345...n

Well, I am trying to write a code that makes the number: $$123456\dots n\tag1$$ So, when $n=10$ we get: $$12345678910$$ And when $n=15$ we get: $$123456789101112131415$$ And when $n=4$ we get: $$1234$$...
• 1,765
144 views

How to use every number between 2^50 and 2^100 without having to rewrite the code? [closed]

What I have currently written returns a numerical value and stores it in b100. p and q are random integers of size 2^50. I want to use the same code to calculate values where p and q ranges from 2^50 -...
• 31
71 views

Inverse/Division in finite field?

Think of multiplictavie group of finite field F[p,n], where p is a prime number and n is a positive integer. The whole elements of F[p,n] can be represented as p^n-p^(n-1) positive integers in the ...
• 3,095
289 views

Largest k such that p^k divides n

(Here all variables are integer.) Is there a built-in function f[n,p] such that f[n,p] = largest k such that p^k divides n For ...
• 3,095
117 views

Approximate integer factorization

Suppose we would like to compute an approximate prime factorization of a large integer x in the sense that the difference between ...
• 409
227 views

How to make a graphic for Sieve of Eratosthenes with a legend

Definition The Sieve of Eratosthenes is a simple algorithm to find the primes before a given $n$. Starting from $n=2$ you delete all multiples of 2, and keep incrementing till all that are left are ...
66 views

Faster Prime[n] for large n, and for n larger than 10^12

Is there a faster implementation of Prime[] available somewhere, already implemented by someone? (Maybe as a compiled routine?) The default function in Mathematica is slow for large values, and does ...
• 622
245 views

How to return two values from function

I have a function that generates cipher text for ElGamal encryption and I want to make return two values, but it returns only one. This is the code: ...
100 views

How to prime factorise rational numbers [closed]

I'm aware of the built-in FactorInteger command for finding the prime factorisation of integers. Is there a convenient way of determining the same thing for a rational number, where the prime ...
• 837
122 views

Factorizing large numbers [closed]

I am trying to factorize large prime numbers with the code bellow. The code works properly for values like 1927 and 69527 (results), but gives no result for larger values like 655051. The code goes as ...
86 views

PrimeQ versus Baillie-PSW primality test [closed]

I read here that Baillie-PSW primality test is proven correct up to $2^{64}$, but I understand PrimeQ is only proven correct up to $10^{16}$, or was that extended ...
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1 vote
49 views

Chinese remainder theorem large modulo [closed]

I have the following modulo congruences: x ≡ 0 (mod 2) x ≡ 2 (mod 5) x ≡ 21 (mod 41) x ≡ 16793129237622992703097532489897447320171386 (mod 648250901^5) I know, ...
55 views

PowerMod solve for b (exponent)

Using PowerMod[a, b, m] = x I get ...
87 views

One 1 minute (mathematica)

I wanna evaluate how large prime numbers my computer work at most 60 seconds. Of course, I can evalutate this manaully e.g. by trying different values. However, can I do this differently, e.g. by ...
265 views

Speeding up FactorInteger for product of two primes

I have a large integer $N$ of size about 10^150. I know that $N$ is a product of two primes $p$ and $q$. I also know that both $p$ and $q$ are of roughly equal size, so one of them is not, for example,...
• 591
1 vote
168 views

Plotting Riemann Prime Counting

I want to program the formula in this page. Didn't take me long to get to my code below. But 1) it only plots the prime counting function and 2) evaluation takes incredibly long. How can I fix it? <...
1 vote
43 views

Geting all prime numbers from the fibonacci sequence in a range of <1000 [closed]

So my attempt was: PrimePi[Fibonacci[Range[1, 999]]] But that doesnt compile into anything. no result no error. i hope one of you got an idea.
• 29
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Goldbach's Conjecture?

If we have a list of even integers, how can we find partitions of size 2, then determine if the partitions are composed of prime numbers? So far, I think I would have to use ...
1 vote
112 views

Find the first 20 primes found by the classical proof of the infinitude of the set of primes

Begin with P={2}; then form,m, the sum of 1 with the product overall elements of P. Place the smallest prime factor of m into P and repeat. Suppose p = {p1,p2,...,pr}, then m = 1+ p1p2p3...pr. Example:...
• 47
269 views

A Wilson prime is a prime p such that (p−1)!≡−1 mod p^2. Write a procedure which determines all Wilson primes less than10^4

I try to use the for loop to solve this question, but it does not work. And here is what I did. For[p = 2,p<=10000,(p-1)! = -1 mod (p^2),Print[p]] I am not sure ...
• 47
84 views

How to write this simple task of unimodular prime search in mathematica?

For testing a particular algorithm I found mathematica is the best way as it has all the tools I need. I am stuck in a number theory part and since I am not an expert in mathematica I do not know how ...
• 135
41 views

Incrementing Numbers

I want to take a prime number p0 = 3, add 2 to it to get a new number p1 = 5, then add four to p1 to get p2, then add 6 to p2 to get p3, etc for a total of 50 times. How do I do that and place my ...
1 vote
60 views

finding primes using chebyshev bias

Using the problem from my previous question link. For each n, that is n= $10^3$ to $10^6$ with a ten-fold increase, how do I use Chebyshev Bias to display the number of primes (which are in the ...
57 views

How do I find how many numbers are prime(taking absolute value of negatives) in a list? When i use count it returns zero

f = 9x^2 - 78x-10000 list1 = PrimeQ[Abs[f /. x -> {Range[1, 20]}]] Count[list1,True] This is my code. Im trying to find how many prime numbers ...
• 363
122 views

Trying to create a list that counts the number primes for each remainder class

Considier the remainder of the first $2500$ prime numbers by the numbers from $3$ to $30$, included. Calculate how many primes are in each remainder class. That is, create a list that for each number ...
1 vote
71 views

A modular version of LinearRecurrence?

I'm playing around with implementing the Lucas probable prime test (mainly so I can understand it better), and would love a version of the LinearRecurrence function that used addition modulo n (with n ...
153 views

203 views

automatic formula finding function [duplicate]

I am curious how easy it would be to automatically find some formulas related to basic number theory OEIS sequences using some Mathematica search algorithm for a small set of OEIS sequences as a ...
• 445
71 views

Prime factorization related functions: prime factor to its power and power of prime [duplicate]

FactorInteger can be used to perform prime factorization: FactorInteger[5^2 7^3 11^4] Results in: ...
• 911
1 vote