Du lette etter:

strong pseudoprime calculator

Strong probable primes and strong pseudoprimes ...
https://mathcrypto.wordpress.com/2014/11/18/strong-probable-primes-and...
18.11.2014 · It can be shown (at least by calculation) that all odd integers less than 2047 are not strong pseudoprime to base 2. In other words, if a positive odd integer is less than 2047 and if it is a strong probable prime to base 2, then must be a prime number. Consider a slightly larger example. Let 65281. Set .
Online calculator: Fermat primality test
https://planetcalc.com/8983
The calculator tests an input number by a primality test based on Fermat's little theorem. Using this calculator, you can find if an input number is Fermat pseudoprime. The calculator uses the Fermat primality test, based on Fermat's little theorem. If n is a prime number, and a is not divisible by n, then : .
Strong Pseudoprime -- from Wolfram MathWorld
mathworld.wolfram.com › StrongPseudoprime
Dec 17, 2021 · If divides exactly one of these factors but is composite, it is a strong pseudoprime. A composite number is a strong pseudoprime to at most 1/4 of all bases less than itself (Monier 1980, Rabin 1980). The strong pseudoprimes provide the basis for Miller's primality test and Rabin-Miller strong pseudoprime test.
Strong probable primes and strong pseudoprimes | Mathematical ...
mathcrypto.wordpress.com › 2014/11/18 › strong
Nov 18, 2014 · The least strong pseudoprime to base 2 is 2047. Note that . Note that the congruences and . The sequence (1) is 1, 1, which is the pattern (1a). Thus 2047 is a strong pseudoprime to base 2. Note that 2047 is composite with factors 23 and 89. It can be shown (at least by calculation) that all odd integers less than 2047 are not strong ...
Pseudo-primes, Weak Pseudoprimes, Strong Pseudoprimes ...
numericana.com/answer/pseudo.htm
10.10.2020 · Poulet numbers are pseudoprimes to base 2. Weak pseudoprimes to base a : Composite integers n dividing ( an - a ). Counting the bases to which a given composite number is a pseudoprime. Strong pseudoprimes to base a are less common than Euler pseudoprimes. The witnesses of a composite number : At least 75% of nontrivial bases.
Strong pseudoprime - Wikipedia
https://en.wikipedia.org › wiki › St...
An odd composite number n = d · 2s + 1 where d is odd is called a strong (Fermat) pseudoprime to base a if:.
Pseudoprime test - Mathematics Stack Exchange
https://math.stackexchange.com › ...
Even better is the strong pseudoprime-test based on fermat's little theorem. ... Let n be a number that we are testing for primality, calculate y=floor(√n) ...
prime numbers - Determine if N is a pseudoprime / strong ...
https://math.stackexchange.com/questions/3517113/determine-if-n-is-a...
21.01.2020 · However that would result in a huge number such as a^15840 which is impossible to calculate. I suppose I should use the fact that 15840 = 2^5 * 495 but I'm not sure how? EDIT: I'm guessing N would be pseudoprime for a base if there's at least one 1, but I'm not entirely sure when it's a strong pseudoprime.
Strong Pseudoprime -- from Wolfram MathWorld
https://mathworld.wolfram.com/StrongPseudoprime.html
17.12.2021 · If divides exactly one of these factors but is composite, it is a strong pseudoprime.A composite number is a strong pseudoprime to at most 1/4 of all bases less than itself (Monier 1980, Rabin 1980). The strong pseudoprimes provide the basis for Miller's primality test and Rabin-Miller strong pseudoprime test.. A strong pseudoprime to the base is also an Euler …
Psedudoprimes - Application Center - Maplesoft
https://www.maplesoft.com › view
97 is a prime Calculate ... Programs to calculate Carmichael numbers ... Strong pseudoprimes are introduced to get a better tool for identifying probable ...
Strong pseudoprime - Wikipedia
https://en.wikipedia.org/wiki/Strong_pseudoprime
A strong pseudoprime is a composite number that passes the Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites also pass, making them "pseudoprimes". Unlike the Fermat pseudoprimes, for which there exist numbers that are pseudoprimes to all coprime bases (the Carmichael numbers), there are no composites that are strong pseudoprim…
Carmichael Numbers Checker - Strong Pseudo-Prime - dCode.fr
https://www.dcode.fr › carmichael-...
Why are the numbers called Carmichael? Carmichael Number Checker. Integer Number (up to 1000 digits) Calculate. See also ...
Rabin-Miller Strong Pseudoprime Test -- from Wolfram MathWorld
mathworld.wolfram.com › Rabin-MillerStrong
Dec 17, 2021 · Rabin-Miller Strong Pseudoprime Test. A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime . It is based on the properties of strong pseudoprimes . The algorithm proceeds as follows. Given an odd integer , let with odd. Then choose a random integer with .
Rabin-Miller Strong Pseudoprime Test -- from Wolfram MathWorld
https://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html
17.12.2021 · Rabin-Miller Strong Pseudoprime Test. A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime . It is based on the properties of strong pseudoprimes . The algorithm proceeds as follows. Given an odd integer , let with odd. Then choose a random integer with .
Strong Pseudoprime -- from Wolfram MathWorld
https://mathworld.wolfram.com › S...
A strong pseudoprime to a base a is an odd composite number n with ... 27) restricts the definition of strong pseudoprimes to only those satisfying (1).
There are infinitely many strong pseudoprimes ...
https://mathcrypto.wordpress.com/2014/11/19/there-are-infinitely-many...
19.11.2014 · Calculate and modulo . Look for the pattern and or the pattern pattern and . If either pattern appears, then is a strong pseudoprime to base . See the sequence labeled (1) in the previous post on strong pseudoprimes. _____ Exercise. Verify that is not a strong pseudoprime to both bases 3 and 5. _____
There are infinitely many strong pseudoprimes | Mathematical ...
mathcrypto.wordpress.com › 2014/11/19 › there-are
Nov 19, 2014 · Calculate and modulo . Look for the pattern and or the pattern pattern and . If either pattern appears, then is a strong pseudoprime to base . See the sequence labeled (1) in the previous post on strong pseudoprimes. _____ Exercise. Verify that is not a strong pseudoprime to both bases 3 and 5. _____
Strong Pseudoprime
https://archive.lib.msu.edu › math
A Composite number is a strong pseudoprime to at most 1/4 of all bases less than itself (Monier 1980, Rabin 1980). The strong pseudoprimes provide the basis for ...
Check if a number is Fermat Pseudoprime - GeeksforGeeks
https://www.geeksforgeeks.org/check-if-a-number-is-fermat-pseudoprime
07.05.2021 · The task is to check whether the number is a Fermat Pseudoprime to the base. The number N is called as Fermat Pseudoprime to the base A, if . 1. A > 1 2. N is a composite number 3. N divides A N-1 – 1.
Strong pseudoprime
https://resources.saylor.org › uploads › 2012/07
In number theory, a strong pseudoprime is a composite number that passes a primality test. All primes pass this test, but a small fraction of composites ...
Check if a number is Fermat Pseudoprime - GeeksforGeeks
https://www.geeksforgeeks.org › c...
The number N is called as Fermat Pseudoprime to the base A, if. 1. A > 1 ... Effectively calculate (x^y) modulo mod.
Fermat primality test - PLANETCALC Online calculators
https://planetcalc.com › ...
Using this calculator, you can find if an input number is Fermat pseudoprime. The calculator uses the Fermat primality test, based on Fermat's little ...
Check if a number is Fermat Pseudoprime - GeeksforGeeks
www.geeksforgeeks.org › check-if-a-number-is
May 07, 2021 · The task is to check whether the number is a Fermat Pseudoprime to the base. The number N is called as Fermat Pseudoprime to the base A, if . 1. A > 1 2. N is a composite number 3. N divides A N-1 – 1. Examples: Input : N = 645, a = 2 Output :1 645 = 3*5*43, Hence it is a composite number Also 645 divides 2^(644)-1 Hence it is a Fermat ...