素数大富豪ディーラー

This app is for enjoying the game "Prime Number Millionaire." It includes the following features:

* Prime Number Determination Mode: Select a card from 1 to K or 0, and the app will determine if it is a prime or composite number. If it is composite, its prime factors will also be displayed.
Prime number determination uses a combination of trial division, Pollard's Rho method, and Miller-Rabin primality test.

* Composite Number Determination Mode: In addition to standard prime number determination, it can also determine if a number is composite.
Enter an equation consisting of multiplication and exponentiation, and the app will determine one of three patterns: "Composite number determined," "Equation not held," or "Factors are not prime."

* Timer Function: A timer can be set from 1 to 5 minutes.

* History Function: You can check the history of your determinations. You can also copy the results as text.

* Prime Number Search Mode: Select any number of cards, and the app will determine whether all permutations and combinations using those cards are prime or composite.

This displays the total number of combinations, the number of prime numbers, the proportion of prime numbers, and a list of prime numbers. This result can also be copied as text.

Due to the heavy processing load, searching with approximately 9-10 cards is the limit.

*Details of Prime Number Determination
Prime and composite numbers are determined using the deterministic Miller-Rabin primality test for all digits. (Probability of false positive: 0)
Specifically, the Miller-Rabin method, using 12 mathematically optimal cardinal numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37), perfectly determines the primeness of integers up to approximately 3 × 10²⁴. For numbers with 26 or more digits, the false positive rate for prime/composite number determination is approximately 6 × 10⁻⁸.

Prime factorization is performed in the following two stages.

① Trial division using prime numbers less than 1 million
② Complete decomposition of the remaining part using Pollard's Rho algorithm
● About Donations
This software accepts donations in the form of in-app items.
You can use all the functions without donating, but donations are greatly appreciated as they motivate the developer.