In the memoirs of Annensky's son, Valentin Krivich, the birth year was stated incorrectly as 1856. From there the date propagated in many biographies. The same incorrect birth year is even stated on Innokenty Anennsky's grave. Only in the 1970s a special archive investigation determined the correct birth year as 1855. See [1]
annensky.lib.ru
V. E. Gitin, “’Intensivnyi metod’ v poezii Annenskogo (Poetika variantov: dva ‘pushkinskikh’ stikhotvoreniia v ‘Tikhikh pesniakh’).” Russkaia literatura, 4, 1997, 34-53