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Mersenne Prime Checker

Run the Lucas-Lehmer test on 2^p - 1 for any exponent p up to 5000, with the digit count, the rank in the known list and the even perfect number it generates.

Related tools

All Numbers & arithmetic tools →
Prime Factor CalculatorFactor any integer up to 10^15 with Pollard's rho and Miller-Rabin, with the factor tree, exponent form, divisor count, sigma and Euler's totient.First n prime numbersList the first n prime numbers — the building blocks of arithmetic that have no divisors but 1 and themselves. Enter how many you want (up to 10,000) and it returns the sequence, the nth prime itself and the sum of them all.List of prime numbersList every prime number up to a chosen limit, using the Sieve of Eratosthenes. Enter an upper bound (up to 100,000) and it returns all primes at or below it, how many there are and their sum — a quick reference for factoring and number theory.Prime factorization calculatorBreak a whole number down into the product of its prime factors.Prime number checkerCheck whether a number is prime and find its smallest divisor.Twin prime finderFind every pair of twin primes up to a limit — primes that differ by exactly 2, like (11, 13) or (17, 19). Enter an upper bound (up to 1,000,000) and it lists the pairs and counts them. Whether infinitely many exist is one of the oldest open problems in mathematics.Amicable Number CheckerCheck whether two numbers are amicable — or give just one and get its candidate partner plus the verified loop, with perfect and sociable numbers identified.Arctan2 Calculator (atan2 of y and x)atan2(y, x) is not atan(y/x): it reads the signs of both arguments to place the angle in the right quadrant over the full −180°…180° turn, and it stays defined when x = 0. Enter x and y, read the angle in degrees or radians, see the quadrant and the point plotted. For a single ratio with no quadrant information, use the arctan calculator instead.

Open Mersenne Prime Checker and you get an answer straight away, with no account to create. It sits under Numbers & arithmetic in our catalogue, alongside Prime Factor Calculator and First n prime numbers.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Mersenne Prime Checker do?

Run the Lucas-Lehmer test on 2^p - 1 for any exponent p up to 5000, with the digit count, the rank in the known list and the even perfect number it generates.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

How is Mersenne Prime Checker different from Prime Factor Calculator?

They sit next to each other but answer different questions: Prime Factor Calculator is the one to open when you need it to factor any integer up to 10^15 with Pollard's rho and Miller-Rabin, with the factor tree, exponent form, divisor count, sigma and Euler's totient. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

First n prime numbers is the closest one after this: List the first n prime numbers — the building blocks of arithmetic that have no divisors but 1 and themselves. Enter how many you want (up to 10,000) and it returns the sequence, the nth prime itself and the sum of them all.

What else is worth having open alongside it?

List of prime numbers and Prime factorization calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Base conversion and number-theory results are exact. Roman numerals follow the standard subtractive form used since the Middle Ages, which is not the only one the Romans themselves used.

Further reading

All guides →
How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.