Bertrand Postulate Checker
Enumerate actual primes in open Bertrand interval (n,2n) for supplied n>1; a finite witness check of an established theorem, not an unproved-conjecture certificate or next-prime alias.
Description
Bertrand's postulate guarantees a prime between n and 2n for integer n>1.
Bertrand's postulate guarantees a prime between n and 2n for integer n>1. A finite sieve can display the witnesses in the caller's requested open interval.1
Enumerate actual primes in open Bertrand interval (n,2n) for supplied n>1; a finite witness check of an established theorem, not an unproved-conjecture certificate or next-prime alias.
When to use Bertrand Postulate Checker
Use this tool to enumerate actual primes in open Bertrand interval (n,2n) for supplied n>1; a finite witness check of an established theorem, not an unproved-conjecture certificate or next-prime alias.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Bertrand Postulate Checker and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter integerN using the field table and calculation rules, then run the tool.
- Read primesStrictlyBetweenNAndTwiceN, observedBertrandIntervalNonempty. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| integerN | Integer n | number | Required |
Enter integer n from 2 to 500,000. Sieve to 2n, exclude both endpoints and return actual primes plus a nonempty flag.
prime interval = (n,2n) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| primesStrictlyBetweenNAndTwiceN | Primes strictly between n and twice n | list of number |
| observedBertrandIntervalNonempty | Observed bertrand interval nonempty | boolean |
{
"input": {
"integerN": 4
},
"output": {
"primesStrictlyBetweenNAndTwiceN": [
5,
7
],
"observedBertrandIntervalNonempty": true
}
}Limitations and assumptions
The output is a finite witness inventory of an established theorem. It is not a next-prime-only operation.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Legendre Conjecture Checker: Enumerate actual primes in one open consecutive-square interval (n²,(n+1)²); coarser distinct interval operation from Oppermann split, not a global Legendre conjecture proof. For a complementary task, use Weak Goldbach Conjecture Checker: Find first nondecreasing prime triple summing to caller odd n>5 using actual sieve and bounded pair search; witnesses may repeat primes, distinct from existing strong two-prime Goldbach partition count.
References
-
Bertrand Postulate Checker — tool.io
Similar or alternative tools
- Legendre Conjecture Checker
Enumerate actual primes in one open consecutive-square interval (n²,(n+1)²); coarser distinct interval operation from Oppermann split, not a global Legendre conjecture proof.
- Weak Goldbach Conjecture Checker
Find first nondecreasing prime triple summing to caller odd n>5 using actual sieve and bounded pair search; witnesses may repeat primes, distinct from existing strong two-prime Goldbach partition count.