How to use the mersenne prime calculator
Prepare the values for this calculation
Calculate Mₚ=2^p−1 for a small prime exponent and test that safe-integer result for primality. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Prime exponent p: enter a value at least 2 and no more than 31 and a whole number. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Mersenne number first. With the unchanged example inputs, it is 8,191. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
The result diagram shows the inputs, method and output. A numeric chart is shown only when the calculation supports a meaningful numeric relationship.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Mersenne Prime Calculator formula
Mₚ=2^p−1; p must be prime.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Prime exponent p | minimum 2; maximum 31; whole number | 13 |
Worked example
Using the example inputs above, the mersenne number is 8,191.
- Mersenne number
- 8,191
- Is Mersenne number prime?
- Yes
Results and assumptions
The output uses the mersenne number convention and formula shown above. Match the entered units and source assumptions when comparing results.
Fix an input or unexpected result
Prime exponent p is required. Enter prime exponent p using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.