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). Composite number is made of its factors (it equals to the product of its factors).
Prime Factorization is about finding not-trivial factors of a natural number if they exist; otherwise, it is a Prime number.
For example, 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 (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).
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.
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 19 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
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 18-digits Prime numbers could be in the range of seconds, depends of the computation power of the hardware.
CPU Speed Test
Factorization of large Prime numbers (see Reference) requires a lot of CPU (processor) power and may serve as a basic “benchmark” reflecting the “number crunching” capability of your hardware (cellphone or tablet). This app implements CPU speed benchmark in Serial and Parallel modes – see sample screenshots taken on 3 different platforms:
1. Huawei Honor 5x (KIW-L24 / Android 6.0.1, API 23)
2. Motorola Moto G (5) Plus (Android 7.0 API 24)
3. Samsung Galaxy Tab 7 (SM-T280 /Android 5.1.1, API 22)
Clearly, parallel algorithms provides tremendous performance boost: for e.g. prime factorization of the largest 15-digit prime takes less than 100 ms on Honor 5x (8-core CPU)
3 largest 14-Digit Prime numbers
3 largest 15-Digit Prime numbers
3 largest 16-Digit Prime numbers
3 largest 17-Digit Prime numbers
3 largest 18-Digit Prime numbers
This app is brought to you by Infosoft International Inc, a NY hi-tech Company providing quality educational resources since 1998. Unique prime factorization algorithm and other major developments are credited to Dr. Alexander Bell, a “Legend” of Codeproject.com, Application Innovation Contest awards winner (AIC 2012 by Intel Corp).
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