Enter an integer to check if it's a Euclid number, or input a range to generate all Euclid numbers within that range.
A Euclid number is defined as \( E_n = P_n\# + 1 \), where \( P_n\# \) represents the product of the first \( n \) prime numbers. Simply put, a Euclid number is formed by adding one to the factorial of the first \( n \) primes.
Prime Factorial: The product of the first \( n \) prime numbers is referred to as \( P_n\# \). Examples include:
Solution:
Calculation:
\( P_1\# = 2 \)
\( E_1 = 2 + 1 = 3 \)
Result: 3 is a Euclid number.
Solution:
Calculation:
\( P_2\# = 2 \times 3 = 6 \)
\( P_3\# = 2 \times 3 \times 5 = 30 \)
\( P_4\# = 2 \times 3 \times 5 \times 7 = 210 \)
\( P_5\# = 2 \times 3 \times 5 \times 7 \times 11 = 2310 \)
Since 2310 is greater than 2023 and 2023 does not equal \( P_n\# + 1 \) for any \( n \), 2023 is not a Euclid number.
Solution:
Calculation:
\( P_2\# = 2 \times 3 = 6 \)
\( P_3\# = 2 \times 3 \times 5 = 30 \)
\( P_4\# = 2 \times 3 \times 5 \times 7 = 210 \)
\( P_5\# = 2 \times 3 \times 5 \times 7 \times 11 = 2310 \)
\( P_6\# = 2 \times 3 \times 5 \times 7 \times 11 \times 13 = 30030 \)
\( 30030 + 1 = 30031 \)
Result: 30031 is a Euclid number.