Input a number to check if it's an interprime, or input a range to generate all interprimes within it.
An interprime is the arithmetic mean of two consecutive odd prime numbers (excluding 2, the only even prime number). If \( p \) and \( q \) are two consecutive odd prime numbers, the interprime can be calculated using the formula: \( \text{Interprime} = \frac{p + q}{2} \) Since \( p \) and \( q \) are prime numbers, their arithmetic mean is never a prime number. Therefore, an interprime is always a composite number.
Solution:
1. Check primality:
234 is not a prime number.
2. Find adjacent primes:
The closest primes to 234 are 233 and 239.
3. Calculate the mean:
\(\frac{233 + 239}{2} = \frac{472}{2} = 236\).
Result: Since \( 234 \neq 236 \), 234 is not an interprime.
Solution:
1. Check primality:
306 is not a prime number.
2. Find adjacent primes:
The closest primes to 306 are 293 and 307.
3. Calculate the mean:
\(\frac{293 + 307}{2} = \frac{600}{2} = 300 \).
Result: Since \( 306 \neq 300 \), 306 is not an interprime.
Solution:
1. Check primality:
2022 is not a prime number.
2. Find adjacent primes:
The closest primes to 2022 are 2017 and 2027.
3. Calculate the mean:
\(\frac{2017 + 2027}{2} = \frac{4044}{2} = 2022\).
Result: Since \( 2022 = 2022 \), it is an interprime.