# 353

This number is a prime.

The smallest smoothly undulating palindromic prime of the form 3(53)_{n}. It is also known as a "sawtooth prime" based on its resemblance to the teeth on the blade of a saw. [Sorensen]

353^{4} = 30^{4} + 120^{4} + 272^{4} + 315^{4}. [Norrie]

353*2^{21} + 1 and 353*2^{369} + 1 are the only
known primes of the form 353*2^{n} + 1. [Melo]

The sum of the first seventeen palindromic numbers, beginning with 0. [De Geest]

The smallest prime for which its 4th power can be written as the sum of 4 integers to the 4th power
(353^{4} = 30^{4} + 120^{4} + 272^{4} + 315^{4}). [Russo]

A multidigit palindromic prime in the decimal expansion of cube root of 44 (a multidigit palindromic number). [Gupta]

The smallest multidigit palindromic prime whose digits are all prime. [Gupta]

The only odd three-digit prime such that the sum of each of its digits raised to itself is prime, i.e., 3^{353} + 5^{353} + 3^{353} is prime. [Opao]

The smallest palindrome that is the sum of 11 consecutive primes (13+17+19+23+29+31+37+41+43+47+53=353). [Schuler]

A palindromic prime obtained from the palindromic expression 3^5 + 35 + 3 - 53 + 5^3. Note that the sum of digits in the expression is 35. [Gallardo]

The sum of the first five primes that are not Chen primes. Note that 353 is a palindromic Chen prime. [Post]

Male ostriches weigh up to 353 pounds. [Snider]

The smallest palindromic prime formed from consecutive primes. [Silva]

The smallest palindromic prime using a prime number of distinct prime digits. Note the prime sum of digits, the prime digital root, the prime additive persistence as well as the prime multiplicative persistence. [Beedassy]

353 = 2^4 + 3^4 + 4^4. [Silva]

The sum of the fourth powers of the digits of 353 is another palindromic prime. [Silva]

Start of the first set of 4 prime-index primes in arithmetic progression, i.e., (353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)). [Jacobs]

The first multidigit palindromic prime to appear in the decimal expansion of *e*. [Gupta]

The only prime-digit palindromic prime that is the first of eight consecutive 3-digit primes, i.e., 353, 359, 367, 373, 379, 383, 389, 397 that remain primes if we delete their first digit, i.e., 53, 59, 67, 73, 79, 83, 89, 97. Note that the sum of the primes of the initial chain is 3000. [Loungrides]

353 is the smallest multi-digit palindromic prime that produces two more palindromes when its prime index, 71, is subtracted or added to it. The next such palindromic prime is 73637. Are there any more? [Gaydos]

If the decimal digits of the current largest known prime were each one inch wide and arranged side-by-side the number would stretch nearly 353 miles.

The smallest palindromic prime formed from odd prime digits. [Silva]

The Country Code of Ireland is 353. [Dowdy]

*Numbers Galore: Perfects, Primes, Triples and
Twins* by Jack McCabe weighs 353 thousandth of an
ounce. [Cardwell]

There were 353 Piggly Wigglys within a year of its opening. [Marshall]