# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 53

• 53 = prime(prime(5) + prime(3)). Note that 53 is the only number with this property
• 53 is the smallest two-digit prime that does not produce a prime by adding a digit to it
• 53 is the smallest multidigit balanced prime: primes which are the averages of their prime neighbors
• 53 is the smallest prime number separated from the preceding and the following prime number by five non-prime numbers (that is 53 is the smallest number in the middle of two sexy prime pairs)
• The month and day are simultaneously prime a total of 53 times in a leap year
• 53 is the smallest prime p such that 1p1, 3p3, 7p7 and 9p9 are all prime
• 53 is the smallest prime which is not the sum or difference between powers of 2 and 3
• 100053 - 53 is prime: note that 53 is the smallest number with this property
• 53 is the only two-digit number that equals its reverse in hexadecimal
• 2 to the power 53 starts with 9: the first time 9 appears as the leading digit of a power of 2. The interesting part is that 9 is the last digit to appear as the leading digit of a power of 2