A deletable prime is a special type of prime number that stays prime even after removing digits one by one, either from the left or right, until only a single-digit prime is left. For example, 31379. Here, removing each digit yields 3137, 313, 31, and 3 (all are Prime). Thus 31379 is deletable prime.
Let's consider an example of 3797:
Since 3797 remains prime after every step of deleting digits, it is called a deletable prime.
Examples of Deletable Primes
Some more examples of Deletable Primes are:
Example 1: 563
563 is prime.
Remove the digit 5 → 63 (prime).
Remove the digit 6 → 3 (prime).
Example 2: 3797
3797 is prime.
Remove the digit 3 → 797 (prime).
Remove the digit 7 → 97 (prime).
Remove the digit 9 → 7 (prime).
Example 3: 233
233 is prime.
Remove the digit 2 → 33 (prime).
Remove the digit 3 → 3 (prime).
First few Deletable Primes are:
2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 157, 163, 167, 173, 179, 193, 197, 223, 229, 233, 239, 263, 269, 271, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439, . . .
Largest Known Deletable Prime
As of October 2024, largest known deletable prime is a 24-digit number: 357686312646216567629137.
Conclusion
In conclusion, a deletable prime is a fascinating type of prime number that remains prime even when its digits are removed one by one, following certain rules. It shows how unique and special Prime Numbers can be.
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