Prime Number Checker

Prime Number Checker is evaluated from Number to Check. The calculation reports Is Prime?, Prime Factorization and All Divisors.

Results

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About the Prime Number Checker

Prime Number Checker is treated here as a quantitative relation between Number to Check and Is Prime?, Prime Factorization, All Divisors and Number of Divisors.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Trial division: test n mod k = 0 for k = 2, 3,..., ⌊sqrtn⌋

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Trial division: test n mod k = 0 for k = 2, 3,..., ⌊sqrtn⌋

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Is 97 Prime?

Inputs

number: 97

Is Prime?: Yes - 97 is prime. Prime Factorization: 97. All Divisors: 1, 97. Number of Divisors: 2. Previous Prime: 89. Next Prime: 101. Prime Index: 25

With Number to Check = 97 as the stated inputs, the result is Is Prime? = Yes - 97 is prime, Prime Factorization = 97 and All Divisors = 1, 97. Each value corresponds to the declared output fields.

Example 2: Is 100 Prime? — Composite

Inputs

number: 100

Is Prime?: No - 100 is composite. Prime Factorization: 2 * 2 * 5 * 5. All Divisors: 1, 100, 2, 50, 4, 25, 5, 20, 10. Number of Divisors: 9. Previous Prime: 97. Next Prime: 101. Prime Index: N/A (not prime)

With Number to Check = 100 as the stated inputs, the result is Is Prime? = No - 100 is composite, Prime Factorization = 2 * 2 * 5 * 5 and All Divisors = 1, 100, 2, 50, 4, 25, 5, 20, 10. Each value corresponds to the declared output fields.

Example 3: RSA Semiprime — Product of Two Primes

Inputs

number: 15

Is Prime?: No - 15 is composite. Prime Factorization: 3 * 5. All Divisors: 1, 15, 3, 5. Number of Divisors: 4. Previous Prime: 13. Next Prime: 17. Prime Index: N/A (not prime)

With Number to Check = 15 as the stated inputs, the result is Is Prime? = No - 15 is composite, Prime Factorization = 3 * 5 and All Divisors = 1, 15, 3, 5. Each value corresponds to the declared output fields.

Example 4: Mersenne Prime? — 127

Inputs

number: 127

Is Prime?: Yes - 127 is prime. Prime Factorization: 127. All Divisors: 1, 127. Number of Divisors: 2. Previous Prime: 113. Next Prime: 131. Prime Index: 31

With Number to Check = 127 as the stated inputs, the result is Is Prime? = Yes - 127 is prime, Prime Factorization = 127 and All Divisors = 1, 127. Each value corresponds to the declared output fields.

Common Use Cases

Check if a number is prime for math competitions
Find prime factors of a number
Generate prime numbers for cryptography
Verify GCD and LCM using prime factors