Largest Prime Number Less Than 1000 Calculator
Search every integer below a selected limit up to 1,000, view prime counts by hundred, and verify why the greatest three-digit prime is 997.
Largest Prime Number Less Than 1000 Calculator inputs
The controls and limits below belong only to this prime calculation.
Largest Prime Number Less Than 1000 Calculator results
How the largest prime number less than 1000 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.
Direct answer
The largest prime number less than 1,000 is 997. It is also the largest three-digit prime. The values 999 and 998 fail immediately: 999 is divisible by 3 and 998 is even.
Why 997 is prime
To prove primality, it is enough to test prime divisors not exceeding √997, which is about 31.6. The relevant primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31. None divides 997.
Exact sieve implementation
Because the complete domain contains only 1,000 integers, the calculator uses an exact sieve rather than a probable-prime test. Every displayed prime and count is therefore exact.
Distribution by hundred
The chart groups primes into 1–99, 100–199 and so on. The bar heights vary because prime occurrence is not uniform over short intervals, even though the long-run density decreases roughly with the logarithm.
Nearby candidates
The result explains why candidates immediately below the selected boundary fail and shows the last primes below it. This makes the answer verifiable instead of presenting 997 as an unexplained fact.
Dedicated search intent
The page combines “largest prime less than 1000,” “largest prime under 1000,” and “largest three-digit prime” into one canonical answer to prevent duplicate pages with identical mathematics.
Largest Prime Number Less Than 1000 Calculator questions
What is the largest prime under 1000?
997.
What is the largest three-digit prime?
997.
Is 999 prime?
No. Its digits sum to 27, so it is divisible by 3.
How many primes are below 1000?
There are 168.