Prime Factorization Calculator Π18

最大18桁の数字の素数分解

INTRODUCTION

A Prime Number is a natural (a.k.a. counting) number that has exactly two distinct divisors called trivial factors, namely: number 1 and itself. Any other factors are considered non-trivial. Any natural number other than Prime is a composite number. Composite numbers are made of their non-trivial factors - they equal to the product of said factors. Number 1 is neither prime nor composite.

OVERVIEW

Prime Factorization is a mathematical task of finding not-trivial factors of any given natural number; if they don't exist then the number under the test is a Prime number.

For example, number 6 has two non-trivial factors 2 and 3, therefore 6 = 2 * 3; number 15 also has two non-trivial factors 3 and 5 (15 = 3 * 5); number 100 has 4 non-trivial factors, namely: 2, 2, 5, 5, thus 100 = 2 * 2 * 5 * 5. On the other side, the Prime numbers 2, 3 and 5 do not have any non-trivial factors: they are evenly divisible (i.e. divisible without remainder) only by the number 1 and the number itself.

Note: in this notation the asterisk "*" means arithmetic multiplication, same as "x" symbol (they can be used interchangeably, thus it could be written: 6 = 2 x 3).

Summary: Prime Numbers do not have any non-trivial factors, like 3, 5, 7 11. Any number with two or more non-trivial factors is called a Composite number, like said number 6, or number 9 (9 = 3 * 3), or 10 (10 = 2 * 5), etc.

USAGE

Calculator is capable of processing large numbers up to 18 digits. To find the prime factors, enter the number in the text box using on-screen keypad and click on enter button "=". Result will appear on digital displaying, showing either the list of found prime factors, or the message indicating that input number is Prime.

PLATFORMS

This app can run in any Cellphone or Tablet equipped with Android 5 or higher.

ALGORITHM

The Calculator utilizes efficient parallel "Wheel Prime Factorization" algorithm optimized for octal-core processors capable of processing large 18-digits numbers in a split second. The actual computation efficiency depends on the platform. The app implements speed test that allows to evaluate device computational power pertinent to Prime factorization heavy number-crunching task. For the reference purpose, largest Prime numbers up to 18-digits are listed below.

REFERENCE

3 largest 14-Digit Prime numbers

99999999999973

99999999999971

99999999999959

3 largest 15-Digit Prime numbers

999999999999989

999999999999947

999999999999883

3 largest 16-Digit Prime numbers

9999999999999937

9999999999999917

9999999999999887

3 largest 17-Digit Prime numbers

99999999999999997

99999999999999977

99999999999999961

3 largest 18-Digit Prime numbers

999999999999999989

999999999999999967

999999999999999877