# 1061

This number is a prime. The smallest bemirp. The sequence begins 1061, 1091, 1601, 1901, 10061, ... . If we are to append to prime 1061 another smallest prime so that the concatenation would yield a square then this second prime would be 10601. Note that 10601 is 1061 with just an extra zero inserted. Also the square root of 106110601 is 10301. Both 10301 and 10601 are palindromic primes! [De Geest] A four-digit prime that equals the number of primes with four digits. [Russo] The Normans conquered Messina in 1061. The first 1061 digits in the decimal expansion of the square root of 10 is prime. [Beedassy] The number of primes between 1000 and 10000 is a bemirp. [Green] The first occurrence of two consecutive emirps (1061, 1069) that remain emirps after having their digits replaced respectively by the corresponding cube and square: (102161, 103681). [Beedassy] The factors of the Mersenne semiprime M1061 each have period length 1061. [Ewing] Can you find the smallest bemirp that has sum of digits equal to 1061? A high school student at Highlands Juvenile Detention Center in Bristol, Virginia, memorized the first 1061 digits in the decimal expansion of π for the 2020 Pi Day celebration.