Fast Prime Calculations
Fastest Prime Number Calculation logic (checks, random generator, prime range generator, primes count generator, summation of primes, factorial of primes, primes generator)
This probably is the BEST solution in the internet as of today 11th March 2022
This same code can be applied in any languages like Python, Go Lang, Java, PHP, Node.js, Javascript, C, C++, .NET, Rust, etc with the same logic and have performance benefits. It is pretty fast based on the number of iterations needed. Performance time checks were not consistent across languages (in my local system - to be direct about wordings). I have not seen this implemented before and has been indigenously done. Feedback and usage is welcome.
Max iterations 16666 for n == 100000 instead of 100000 of conventional way. The iterations counts for different ways for Prime number check 100007 can be seen as follows:
count: Prime Conventional way for 83 is 81
Is Prime 83 isPrimeConventionalWay: True
count: Prime Squareroot way 83 is 8
Is Prime 83 isPrimeSquarerootWay: True
count: Prime Unconventional way for 83 is 14
Is Prime 83 prime (SUGGESTED): True
count: Prime AKS - Mersenne primes - Fermat's little theorem or whatever way 83 is 2
Is Prime 83 isprimeAKSWay: True
count: Prime Conventional way for 169 is 12
Is Prime 169 isPrimeConventionalWay: False
count: Prime Squareroot way 169 is 12
Is Prime 169 isPrimeSquarerootWay: False
count: Prime Unconventional way for 169 is 1
Is Prime 169 prime (SUGGESTED): False
count: Prime AKS - Mersenne primes - Fermat's little theorem or whatever way 169 is 4
Is Prime 169 isprimeAKSWay: False
count: Prime Conventional way for 100007 is 96
Is Prime 100007 isPrimeConventionalWay: False
count: Prime Squareroot way 100007 is 96
Is Prime 100007 isPrimeSquarerootWay: False
count: Prime Unconventional way for 100007 is 15
Is Prime 100007 prime (SUGGESTED): False
count: Prime AKS - Mersenne primes - Fermat's little theorem or whatever way 100007 is 32
Is Prime 100007 isprimeAKSWay: False
count: Prime Conventional way for 300530164787 is 1180
Is Prime 300530164787 isPrimeConventionalWay: False
count: Prime Squareroot way 300530164787 is 1180
Is Prime 300530164787 isPrimeSquarerootWay: False
count: Prime Unconventional way for 300530164787 is 196
Is Prime 300530164787 prime (SUGGESTED): False
count: Prime AKS - Mersenne primes - Fermat's little theorem or whatever way 300530164787 is 393
Is Prime 300530164787 isprimeAKSWay: False
Code Base
Javascript
- Access Node code using require("fast-prime")
- Access client (browser code) for just basic prime checks using
./node_modules/src/client/primes.jsandnode_modules/src/client/primes.min.js - Access client (browser code) using
./node_modules/src/client/primes.all.jsandnode_modules/src/client/primes.all.min.js - Access client (browser code) using cdn
https://unpkg.com/fast-prime@{version}/src/client/primes.all.js. Examplehttps://unpkg.com/fast-prime@0.0.64/src/client/primes.all.min.js - Access client (browser code) smaller non optimised size using
./node_modules/src/client/primes.ip.jsandnode_modules/src/client/primes.ip.min.js - Access client (browser code) smaller non optimised using cdn
https://unpkg.com/fast-prime@{version}/src/client/primes.ip.js. Examplehttps://unpkg.com/fast-prime@0.0.64/src/client/primes.ip.min.js - Demos
Features of the Library
-
Different ways of prime number checks (isprime)
- Fast prime (Recommended innovative function) - Iterative/Recursive (Conventional iterative way) - SquareRoot (AKS - Mersenne primes - Fermat's little theorem) -
Different ways of getting primes (using all above different ways)
- Fetch prime between two number range (min - max) - Fetch counts (numbers) of prime starting from any number - Random prime number generator [TODO] - Optimized function with pre-calculated stored values (< 10000, < 100000, < 1000000) - Stored value calculation Failover to JIT calculation using above formulaes -
Different ways of getting summation of primes (using all above different ways)
- Fetch summation of prime between two number range (min - max) - Fetch summation of counts (numbers) of prime starting from any number - Fetch summation of Custom array provided [TODO] - Fetch factorial - Optimized function with pre-calculated stored values (< 10000, < 100000, < 1000000) - Stored value calculation Failover to JIT calculation using above formulaes -
Different ways of getting factorial of primes (using all above different ways)
- Fetch factorial of prime between two number range (min - max) - Fetch factorial of counts (numbers) of prime starting from any number - Fetch factorial of Custom array provided [TODO] - Fetch factorial - Optimized function with pre-calculated stored values (< 10000, < 100000, < 1000000) - Stored value calculation Failover to JIT calculation using above formulaes
// Usage API for client
// Check demos folder for usage in the github repos
// https://github.com/ganeshkbhat/fastprimenumbers/tree/main/nodejs/demos
primes().fast // Recommended or Suggested way
primes().primes // Recommended or Suggested way
primes().recursive
primes().sqrootExpressive
primes().sqroot
primesCount().alternateWays
primesCount().alternateWaysOptimized (async - promise)
primesCount().fast
primesCount().fastOptimized (async - promise)
primesRange().alternateWays
primesRange().alternateWaysOptimized (async - promise)
primesRange().fast
primesRange().fastOptimized (async - promise)
primesSum().alternateWaysCount
primesSum().alternateWaysCountOptimized (async - promise)
primesSum().alternateWaysRange
primesSum().alternateWaysRangeOptimized (async - promise)
primesSum().fastCount
primesSum().fastCountOptimized (async - promise)
primesSum().fastRange
primesSum().fastRangeOptimized (async - promise)
primesFactorial().factorial
primesFactorial().alternateWaysCount
primesFactorial().alternateWaysCountOptimized (async - promise)
primesFactorial().alternateWaysRange
primesFactorial().alternateWaysRangeOptimized (async - promise)
primesFactorial().fastCount
primesFactorial().fastCountOptimized (async - promise)
primesFactorial().fastRange
primesFactorial().fastRangeOptimized (async - promise)
Python
Stack overflow Link for Calculations
LICENSE
Custom Crediting License PROPRIETARY LICENSE AGREEMENT ONLY
TODO
- [D] Add summation of array of primes using (range, count)
- Add summation of array of primes using custom prime numbers
- [D] Add factorial of array of primes using (range, count)
- Add factorial of array of primes using custom prime numbers
- Consider adding random prime generator
- Consider adding generator using generator functions
- [D] Consider adding fetching primes from remote api for stored primes
- Consider adding support for very large prime numbers (checks, range, count, sum, factorial, random) and related generators
- Consider adding support for very large random prime generator
- Adding following (all) APIs to Javascript, Typescript, Python, Java
- Adding all APIs to Go, TS (Consider C#, Rust, C, Cpp)
- Consider adding function to library