New Rules for Calculating Decimal Number Residue on Primes

Cryptography is critical to guaranteeing the security of information transmitted via the internet. Prime numbers are a critical component of any cryptographic system and play a crucial part in guaranteeing the system’ s security. Currently, several algorithms are employed to determine whether a given number is prime or not. Some of the most often used algorithms include the Divisibility Test, the Fermat Test, and the Chinese Primality Test. This article reveals new rules to calculate the decimal residue over prime number in modular arithmetic which applies also as divisibility test. The proposed methodology segregates the decimal number into blocks with equal size specific for each prime, and then substitutes each digit with an integer, where the sum of those integers yields the residue. The methodology was proved mathematically. Practical tests show that this methodology is valid for a long range of decimals, with realistic number of rounds. Further to that manual calculation samples have been demonstrated.