Formula
For prime p and a not divisible by p, a^(p−1) mod p=1.
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- p is independently checked by trial division; the theorem is not used as a primality test.
Example Calculation
Example inputs
- Integer a: 2
- Prime p: 7
Integer a = 2; Prime p = 7. Primary result: 1.
Frequently asked questions
How do I use this calculator?
Enter integer a, prime p. The result updates automatically. Use Reset to restore the example values.
What method does it use?
For prime p and a not divisible by p, a^(p−1) mod p=1.. p is independently checked by trial division; the theorem is not used as a primality test.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.