# 2221

This number is a prime.

2221 and 2^{2221} - 2221^{2} are both prime. [Luhn]

The next prime happy-go-lucky year will be 2221. The number 2221 is simultaneously a happy number and a lucky number.

The smallest prime such that if reduced by one, has 1, 2 and 3-digit factors. [Gallardo]

2221 = 1^2 + 1^3 + 2^5 + 3^7 is the sum of the first 4 positive Fibonacci numbers raised to the powers of the first 4 primes. Curiously, it is concatenated from entirely Fibonacci number digits. Note that 2221 is prime. [Post]

The number of positive-integer Proximate-Prime Polynomials derived from 4 successive primes under 1000000. [Capelle]

The smallest Honaker prime formed by concatenating two consecutive numbers. [Loungrides]

The smallest prime formed from two successive double-digit composite numbers. [Loungrides]

The smallest Honaker prime with sum of digits equal to 7. Are there any more? [Gaydos]

The smallest Honaker prime with no digits greater than 2. The next one is 22221211. [Gaydos]

The smallest prime of the form 2^2+2^3+2^5+2^7+2^11+1, where the exponents are consecutive palindromic primes. [Sariyar]

The smallest Honaker prime with a prime index (331) whose own index is also prime (67). Note that 67 also has a prime index (19). [Homewood]

2221, 2239, and 2251 are the first case of three consecutive lucky numbers all being primes. [Gaydos]

10^1000 is probably in a prime gap of length 2221. Found using n(10^1000)-b(10^1000)-1 at Apertron. [Gaydos]