11011...00111 (1601-digits)

This number is a prime.

Let z(s) be the number 11011100101 ... , concenating the binary representation of the numbers 1 to s. So, z(4)=11011100. Now, the number above is z(231), the smallest prime of this form. It has 1601 digits, which is also a prime. Moreover, 231 has a palindromic binary representation. [Wallrodt]