Prime Factorization Calculator "Prime P15"

包括的な15桁までの自然数の素因数分解

Attn. NEWER MODEL P18 (UP TO 18-DIGITS) AVAILABLE: https://play.google.com/store/apps/details?id=biz.infosoft.prime18

OVERVIEW

A Prime Number is a natural (a.k.a. counting) number that has exactly two distinct divisors (factors): number 1 and itself, called trivial factors. Any other factors are considered non-trivial and any natural number other than Prime is a composite number (number 1 is neither prime nor composite). Prime Factorization is about finding not-trivial factors of a natural number if they exist; otherwise, it is a Prime number.

For e.g., number 6 has two non-trivial factors: 2 and 3 (in other words, 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 numbers 2, 3 and 5 do not have any non-trivial factors: they are evenly divisible 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).

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

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.

Calculator is capable of processing large numbers up to 15 digits. Be aware that calculation of such big numbers may take several seconds, depends on how fast is the cellphone CPU (processor) - for more details see the following Benchmarks chapter

PLATFORMS

This app can run in any Cellphone or Tablet equipped with Android 5 or higher (i.e. Android Lollipop / Marshmallow / Nougat / Oreo). Prime factoring algorithm implements heavy "number crunching", so the computation time for large 15-digits Prime numbers could be in the range of seconds, depends of the computation power of the hardware.

Benchmarks

The factoring of the large Prime numbers (see the Reference) may serve as a basic "benchmark" reflecting the number crunching capability of your hardware (cellphone or tablet). For example, taking the largest 15-Digit Prime number: 999999999999989 and testing it on 3 different Android hardware platforms, the calculation time estimates:

Cellphones

1. Huawei Honor 5x (KIW-L24 / Android 6.0.1, API 23) - approx: 1 sec

2. Motorola Moto G (5) Plus (Android 7.0 API 24) - calculation time approx: 3 sec

Tablet

3. Samsung Galaxy Tab 7 (SM-T280 /Android 5.1.1, API 22) - approx: 10 sec

Clearly, the relatively new cellphones (1, 2) perform the Prime "number crunching" much faster than the old version of Samsung Galaxy Tab 7.

REFERENCE

5 largest 15-Digit Prime numbers

999999999999989

999999999999947

999999999999883

999999999999877

999999999999827

5 largest 14-Digit Prime numbers

99999999999973

99999999999971

99999999999959

99999999999931

99999999999929

ABOUT

Prime Factoring Calculator "Prime P15" is brought to you by Infosoft International Inc, a NY hi-tech Company providing quality educational resources since 1998. All major developments are credited to Dr. Alexander Bell, a "Legend" of Codeproject.com, Application Innovation Contest awards winner (AIC 2012 by Intel Corp). Calculator is powered by unique computation engine developed personally by Dr. Bell and implemented in award-winning app "Edumatter" for Windows available at http://shopdigit.com/Edumatter-814-Standard-for-Win-M814-1.htm (up to 18 Digits) and educational web portal http://examn8.com/Primes.aspx (up to 16 Digits)

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