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4
votes
2answers
100 views

Generating numbers palindromic in two number bases

The purpose of the code below is to generate numbers that are $2d+1$ digit palindromes in number base $b+1$, and are also palindromic in number base $b+3$, where: The ...
3
votes
1answer
187 views

Generation of Step Numbers

I am working on Project Euler 178 but got stuck in trying to optimize my code. The following text comes from the problem: Consider the number $45656$. It can be seen that each pair of ...
6
votes
1answer
108 views

Efficient way to sum all divisors of numbers below N excluding divisors 4/d

So, I want to Sum all divisors off all numbers below N (for a big N, i.e. N=10^16) which (divisors) are NOT a multiple of 4 I tried DivisorSigma but then the following method was x2 faster ...
3
votes
0answers
115 views
16
votes
1answer
206 views

Is it better to completely forget about the existence of PowersRepresentations?

I noticed that in several cases the performance of PowersRepresentations is hugely worse than that of IntegerPartitions. (Mma 10....
2
votes
1answer
135 views

Twin Prime Max Gaps (Performance Tuning)

Ok, let's build a foundation here: A common way of testing primality, is dividing by all primes smaller than the number's square root. For instance, $97$ is prime because dividing by none of the ...
6
votes
1answer
146 views

Faster square test for integers

This question was asked already in Jan '12 and the most recent answer is from Oct '12, so it's several Mathematica versions out of date. What is a faster test for whether an integer is a perfect ...
24
votes
3answers
566 views

Speeding up the built-in Rudin-Shapiro and Thue-Morse sequence functions

Version 10.2 introduced two well-studied sequences as functions: the (Golay-)Rudin-Shapiro sequence (RudinShapiro[]) and the (Prouhet-)Thue-Morse sequence (...
4
votes
1answer
234 views

How to further accelerate arithmetic with Fermat Pseudoprime and Fibonacci number

I've been working on this all night, and I have made this go pretty fast, compared to my first iteration of the program, but now I'm out of ideas. I'm trying to write a program to test (by good old ...
9
votes
2answers
510 views

Number of divisors visualized with the QPochhammer function, how to improve performance of code?

I have this code that is originally Jeffrey Stopple's code for the Riemann zeta function in the complex plane. Because I discovered yesterday that the number of divisors can be generated with the $q$-...
5
votes
1answer
204 views

Ruth-Aaron quadruple challenge

This a computational challenge, to find an efficient algorithm to discover a quadruple $(n,n+1,n+2,n+3)$ with the same sum of prime factors as described in the MO question, "Ruth-Aaron triples, etc." ...
2
votes
3answers
181 views

Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
18
votes
7answers
2k views

Integers which are the sum of both two and three consecutive squares

This is a math problem I came across the other day: $365$ can be written as a sum of two and also three consecutive perfect squares: $$365=14^2+13^2=12^2+11^2+10^2$$ What is the next number with ...
14
votes
2answers
968 views

the more effective method to find 21 digits armstrong number

In recreational number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number(after Michael F. Armstrong) or a plus perfect number) is a number that is ...
12
votes
1answer
349 views

Is there a PrimeQ whose accuracy guarantee you can adjust?

Say I have a list of a million integers each with a million digits, and I want a crude sieve to see which have a chance at being prime. Mathematica has a PrimeQ function, which appears to be slow ...
2
votes
0answers
116 views

Approximate to the speed of Built-In functions

In Mathematica, there is a function PowerMod[a,b,m], which computes a^b mod m. I will concern only this case: ...
4
votes
3answers
637 views

Why is my solution to PE #5 so slow

I'm new to Mathematica and it was suggested to me to go through the Project Euler problems in order to learn it. However, I can't quite figure out why my solution to #5 is so slow. The problem: ...
3
votes
1answer
247 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
6
votes
2answers
421 views

Memory management and speed for Fast GCD

Let's say that we have some $300\,\text{K}$ digits (arbitrary function) and want to trial factor with $100{,}000{,}000$ first prime numbers. ...
11
votes
2answers
872 views

Modular arithmetic - efficiently calculating the remainders of factorials

When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code. ...
5
votes
2answers
391 views

How can this DivisorSigma code be made fast?

Since Project Euler problems are now fair game for questions I have a question of my own. A certain problem* states: For a positive integer n, let σ2(n) be the sum of the squares of its divisors. ...
11
votes
3answers
4k views

Easier program for period of Fibonacci sequence modulo p

For a little project I need to calculate the period of a Fibonacci sequence modulo p, for which p is a prime number. For example, the Fibonacci sequence modulo 19 would be: $$0, 1, 1, 2, 3, 5, 8, 13, ...
1
vote
1answer
297 views

Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...
15
votes
2answers
580 views

Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
13
votes
2answers
809 views

FiniteFields package is very slow. Any fast substitute for Mathematica?

I want to compute the inverse of matrix, say with dimensions $100 \times 100$, defined over a large finite field extension such as $GF(2^{120})$. I am using the package FiniteFields, but Mathematica's ...
26
votes
1answer
4k views

Finding long strings of identical digits in transcendental numbers

Introduction Describing the three main streams of present-day mathematical philosophy (formalism, Platonism and intuitionism) in a well-known book, The Emperor's New Mind, R. Penrose says: ...it ...
27
votes
7answers
3k views

Efficient way to count the number of zeros at the (right) end of a very large number

If I want to count the number of zeros at the (right) end of a large number, like $12345!$, I can use something like: Length[Last[Split[IntegerDigits[12345!]]]] ...
18
votes
6answers
3k views

Fastest square number test

What is the fastest possible square number test in Mathematica, both for machine size and big integers? I presume starting in version 8 the fastest will be a dedicated C LibraryLink function.