Largest Prime Number in Range Calculator
Search a finite interval, identify its greatest prime, count primes when an exact segmented search is practical, and visualize their distribution.
Largest Prime Number in Range Calculator inputs
The controls and limits below belong only to this prime calculation.
Largest Prime Number in Range Calculator results
How the largest prime number in a range tool works
This page targets one distinct largest-prime search intent. It separates finite answers, known records, probable-prime status and formal proof instead of merging them into a generic prime checker.
Range search rather than an infinite record
The interval supplies both a lower and upper boundary, so the greatest prime is well defined. The calculator automatically orders reversed endpoints and reports when no prime occurs inside the selected interval.
Exact sieve mode
When the endpoints and width fit the exact browser limits, a sieve marks every prime in the range. This permits an exact count, first prime, largest prime and distribution histogram rather than only a single descending search result.
Large-integer mode
For larger BigInt endpoints, the engine searches downward for the greatest prime without pretending to count every prime in the interval. The output labels whether the primality test is deterministic or probable.
Endpoint rules
Both endpoints are included. A prime equal to the upper endpoint is therefore the largest result immediately. To exclude the upper boundary, use the less-than-N calculator.
Prime-density visual
The histogram groups the interval into equal-width bins. It shows where primes occurred in the selected range, but it is not evidence of a permanent pattern. Prime distributions fluctuate over short intervals.
Performance limits
The maximum-width input is part of the mathematical specification. It prevents accidental requests for billions of candidate checks in one browser tab and makes incomplete searches explicit.
Largest Prime Number in Range Calculator questions
Are both endpoints included?
Yes.
What happens if start is greater than end?
The calculator reorders them before searching.
Can a range contain no prime?
Yes, especially very short intervals inside a prime gap.
Why is prime count sometimes unavailable?
For giant BigInt ranges, the calculator finds the largest candidate without claiming that it enumerated the entire interval.