Discover the largest prime hidden within any limit. Adjust lower and upper bounds to control your search. Instantly see computations, divisibility checks, and timing details organized. Export result history as structured CSV or PDF snapshots. Designed for deeper number theory exploration and classroom demonstrations.
A prime number is a positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself.
This calculator uses these steps to find the largest prime:
The first candidate that passes all tests is reported as the largest prime inside the requested interval.
Submit the form to see the largest prime in your range.
Your calculation history will appear here after you run computations.
For very large ranges, computations may take longer because the algorithm must perform more divisibility checks before finding a suitable prime.
Suppose you want to find the largest prime less than or equal to 250 and also inspect how primes are distributed inside this range.
The calculator reports that the largest prime not exceeding 250 is 241. The prime statistics show how many primes appear between 2 and 250, the interval length, and the average density.
The prime list box displays the primes from 2 up to 241, allowing you to scroll, inspect gaps, and compare values with the statistics shown alongside the main result.
| Example | Lower limit | Upper limit | Largest prime | Notes |
|---|---|---|---|---|
| Example 1 | 2 | 100 | 97 | Largest prime not exceeding one hundred. |
| Example 2 | 50 | 80 | 79 | Search restricted to a mid-sized sub-range. |
| Example 3 | 990 | 1020 | 1019 | Shows behavior near a thousand-scale interval. |
The largest prime below a limit N is the greatest integer p such that p is prime and p ≤ N. This calculator scans downward from N, testing candidates until it finds the first number that passes the primality checks and satisfies this condition.
By enabling detailed statistics, you can see how often primes occur inside any interval, measure the size of the largest gap between consecutive primes, and compare the gap immediately before the largest prime with other gaps found in the same search range.
Largest primes in specific ranges are useful when designing keys for cryptographic schemes, constructing hashing schemes, and building randomization routines. Educators can also rely on this calculator to quickly generate nontrivial prime examples for problem sets, quizzes, and classroom demonstrations.
Running multiple searches over different lower and upper limits allows you to compare prime densities side by side. Smaller intervals near the same scale can show how local prime behavior fluctuates, while broad intervals highlight long-range trends in how tightly primes are clustered together.
The algorithm is optimized with square-root bounds and a 6k ± 1 pattern, but very large N still require many divisibility checks. Use the timing output to understand computational cost and adjust ranges, or disable extra statistics when exploring extremely large intervals.
The history table records every run, including limits, result, and timing. Exporting this information as CSV lets you visualize prime search performance in spreadsheets, while PDF snapshots preserve complete experiment logs that can be shared with collaborators, students, or research supervisors.
It finds the largest prime number in a chosen interval. You specify a maximum N and optional minimum. The tool scans downward from N, testing candidates, and returns the greatest value that passes the primality checks inside that range.
That depends mainly on your server resources and time limits. The algorithm is efficient but still needs many divisions for big N. Start with modest ranges, observe timing output, then gradually increase N while monitoring page responsiveness.
Listing primes lets you inspect actual values inside the interval. Statistics summarize how primes behave: counts, density, largest gaps, and neighbor relationships. Turning them off keeps the interface lighter and speeds calculations for very large search ranges.
This tool is good for educational exploration but not a full cryptographic library. Serious cryptographic systems require carefully audited randomness, massive primes, and side-channel protections. Always rely on well-maintained security libraries instead of browser forms for real cryptographic workflows.
Reduce the upper limit or narrow the interval between lower and upper bounds. Disable extra statistics and prime listing, then rerun. If problems continue, reload the page to clear history and start again with smaller, safer test values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.