9999999900000001
This number is a prime.
91 is composite, 9901 is prime, 999001 is composite, 99990001 is prime, 9999900001 is composite, 999999000001 is prime, 99999990000001 is composite, 9999999900000001 is prime. Unfortunately, the next two terms in this sequence are each composite. [Beiler]
The greatest prime factor of any 48-digit repdigit is
9999999900000001. [Green]
9999999900000001 is the 8th known prime, p, such that
(p)2 divides (p)3. Can you find other cases like this? [Green]
9999999900000001 is a prime number such that p^2 is a sibling number type (a+1).a, where dot is for concatenation: 9999999900000001^2 = 9999999800000002.9999999800000001. [Rivera]
9999999900000001 = 10^8+99999999^2, 999999000001 = 10^6+999999^2, 99990001 = 10^4+9999^2, 9901 = 10^2+99^2 are the unique expressions (as sums of squares) of four primes. Very likely theses are the only primes of this form. [Kuhn]
91 is composite, 9901 is prime, 999001 is composite,
99990001 is prime, 9999900001 is composite, 999999000001 is
prime, 99999990000001 is composite, 9999999900000001 is
prime. Now rewriting the digits of these numbers from right
to left we have, 19 is prime, 1099 is composite, 100999 is
prime, 10009999 is composite, 1000099999 is prime,
100000999999 is composite, 10000009999999 is composite,
1000000099999999 is composite. All the composite numbers in
the progression have two prime factors except
10000009999999 having three, 1000000099999999 having four [Nwamba]
9999999900000001 = 99999999^2 + 99999999^1 + 99999999^0. [Nwamba]