veprimes
A veprime is a prime number $p$ such that $p^2$ has the same number of digits as $p$ in base 10. For example, the prime number 2 has one digit, and $2^2 = 4$ also has one digit. Similarly, the prime number 3 has one digit, and $3^2 = 9$ also has one digit. However, the prime number 5 has one digit, and $5^2 = 25$ has two digits, so 5 is not a veprime.
The condition for a prime number $p$ to be a veprime can be expressed mathematically. Let $d(n)$
The first few veprimes are 2, 3, 5, 7. For these single-digit primes, their squares (4, 9,
As prime numbers increase in size, their squares tend to grow much faster, resulting in more digits.