Emirps

An emirp is a type of prime number that, when its digits are reversed, still results in a prime number, but the reversed number must be different from the original one. The word "emirp" comes from the word "prime" spelled backwards.

Example:

• 13 is an emirp because when reversed, it becomes 31, which is also a prime number.
• 17 is an emirp because its reverse, 71, is also prime.

Properties of Emirps:

• An emirp is always a two-digit or larger prime number.
• An emirp is not a palindrome (a number that is the same forwards and backwards). For example, 131 is not an emirp because it is the same when reversed.
• The smallest emirp is 13.

List of emirps

(13, 31), (17, 71), (37, 73), (79, 97), (107, 701), (113, 311), (149, 941), (157, 751), (179, 971), (199, 991), (337, 733), (347, 741), (359, 953), (389, 983), (709, 907), (739, 937), (769, 967), (1009, 9001), (1021, 1201), (1031, 1301), (1033, 3301), (1061, 1601), (1069, 9601), (1091, 1901), (1097, 7901), (1103, 3011), (1109, 9011), (1151, 1511), (1153, 3511), (1181, 1811), (1193, 3911), (1213, 3121), (1217, 7121), (1223, 3221), (1229, 9221), (1231, 1321), (1237, 7321), (1249, 9421), (1259, 9521), (1279, 9721), (1283, 3821), (1381, 1831), (1399, 9931), (1409, 9041), (1429, 9241), (1439, 9341), (1453, 3541), (1471, 1741), (1487, 7841), (1499, 9941), (1523, 3251), (1559, 9551), (1583, 3851), (1597, 7951), (1619, 9161), (1657, 7561), (1669, 9661), (1723, 3271), (1733, 3371), (1753, 3571), (1789, 9871), (1847, 7481), (1867, 7681), (1879, 9781), (1913, 3191), (1933, 3391), (1949, 9491), (1979, 9791), etc...

Conclusion

Emirps are part of a special group of numbers called "reversible primes," and they are studied in number theory, a branch of mathematics.