Sayyiduna Anas (Radi Allahu Anhu) has reported that the beloved Prophet (SallAllahu Alayhi wa Sallam) said,
Anyone who observes a fast in the month of Rajab; it will be like fasts of one year. Whosoever observes seven fasts, the seven doors of Hell will be closed for him, whosoever observes eight fasts, the eight portals of Heaven will be opened for him, anyone who observes ten fasts, whatever he beseeches before Allah, it will be granted to him. And, whosoever observes 15 fasts, a heavenly herald announces, ‘Your past sins have been forgiven; therefore you commence deeds afresh as your evil deeds have been replaced by good deeds.’ And whosoever does more, may Allah grant him more. Sayyiduna Nuh (Alayhis Salam) stepped onto his Ark in Rajab; he himself observed fast and ordered his fellow-voyagers to observe fast too. His Ark travelled for six months until the 10th of Muharram al-Haraam.
[Bayhaqi, Shu’ab al-Iman, Vol. 3, Page 368, Hadith 3801]