Find the nearest surrounding primes and their gap around n
Result
Answer
Step-by-Step Derivation
Prime Gap Formula
Prime gap = next prime - previous prime
For consecutive primes p_k and p_(k+1): gap = p_(k+1) - p_k
A prime gap measures the distance between prime numbers. This calculator searches around the entered value to identify the nearest primes and subtracts them to show the local gap.
⚠This browser tool accepts n from 2 to 1000000. Very large prime gap research requires stronger primality and search methods.
What Is a Prime Gap?
A prime gap is the difference between prime numbers. Studying these gaps helps reveal how primes thin out and cluster as numbers grow larger.
Previous Prime
Search downward from n until a prime is found.
Next Prime
Search upward from n until a prime is found.
Gap Value
Subtract previous prime from next prime.
Distribution Insight
Large and small gaps show patterns in prime spacing.
Example: For n = 100, the previous prime is 97 and the next prime is 101, so the local prime gap is 101 - 97 = 4.
Applications of Prime Gaps
Nearest PrimePrime DistributionAnalytic Number TheoryAlgorithm TestsContest Math
Frequently Asked Questions
What is a prime gap calculator?▼
It finds nearby prime numbers around n and calculates the difference between the previous prime and next prime.
What is the prime gap formula?▼
A prime gap is usually written g = p_next - p_previous for consecutive or surrounding primes.
How do I use this nearest prime calculator?▼
Enter n and calculate. The tool searches downward and upward for primes, then subtracts them to find the gap.
What happens if n is already prime?▼
If n is prime, it can be both the previous and next prime in this surrounding-prime version, giving gap 0 at that exact point.
Where are prime gaps used?▼
Prime gaps are used in prime distribution research, analytic number theory, algorithm testing, and contest problems about nearest primes.
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