Abd al-Aziz narrates from his father, Sayyiduna Sa'id (may Allah be pleased with him) (Uthman said that his father had the companionship of the Prophet); he said that the Messenger of Allah (peace and blessings be upon him) said: "Rajab is a mighty month; in it Allah multiplies the good deeds. Whoever fasts one day of Rajab, it is as if he has fasted a year; whoever fasts seven days of it, the seven gates of Hell are closed to him; whoever fasts eight days of it, the eight gates of Paradise are opened for him; whoever fasts ten days of it, whatever he asks of Allah, Allah grants it to him; and whoever fasts fifteen days of it, a caller calls out from the heaven: 'Your past sins have been forgiven, so begin your deeds afresh.' And whoever does more, Allah, the Mighty and Majestic, gives him more. And it was in Rajab that Allah carried Sayyiduna Nuh (peace be upon him) in the Ark, so he fasted Rajab and ordered those with him to fast. The Ark sailed with them for six months, and at the end of that, on the day of Ashura, it came to rest on al-Judi. So Nuh (peace be upon him) and those with him, and the animals too, fasted out of gratitude to Allah, the Mighty and Majestic. On the day of Ashura Allah split the sea for the Children of Israel; on the day of Ashura Allah, the Mighty and Majestic, accepted the repentance of Adam (peace be upon him) and of the people of Yunus (peace be upon him); and on that day Ibrahim (peace be upon him) was born."
Hadith Referenceالمعجم الكبير للطبراني / باب السين / 5517