Definition:Two-Sided Prime
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Definition
A two-sided prime is a prime number which remains prime when:
- any number of digits are removed from the left hand end
and:
- any number of digits are removed from the right hand end
but, generally, not from both ends at once.
Sequence
The complete sequence of two-sided primes is:
- $2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739 \, 397$
Examples
$739 \, 397$ is a Two-Sided Prime
| \(\ds 739 \, 397\) | \(\) | \(\ds \) | is the $59 \, 489$th prime | |||||||||||
| \(\ds 39 \, 397\) | \(\) | \(\ds \) | is the $4148$th prime | |||||||||||
| \(\ds 9397\) | \(\) | \(\ds \) | is the $1162$nd prime | |||||||||||
| \(\ds 397\) | \(\) | \(\ds \) | is the $75$th prime | |||||||||||
| \(\ds 97\) | \(\) | \(\ds \) | is the $25$th prime | |||||||||||
| \(\ds 7\) | \(\) | \(\ds \) | is the $4$th prime |
| \(\ds \) | \(\) | \(\ds 739 \, 397\) | is the $59 \, 489$th prime | |||||||||||
| \(\ds \) | \(\) | \(\ds 73 \, 939\) | is the $7296$th prime | |||||||||||
| \(\ds \) | \(\) | \(\ds 7393\) | is the $939$th prime | |||||||||||
| \(\ds \) | \(\) | \(\ds 739\) | is the $131$st prime | |||||||||||
| \(\ds \) | \(\) | \(\ds 73\) | is the $21$st prime | |||||||||||
| \(\ds \) | \(\) | \(\ds 7\) | is the $4$th prime |
$\blacksquare$
Also see
- Results about two-sided primes can be found here.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $739,397$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $739,397$