Abd al-Aziz bin Sa'id reports this statement from his father (the narrator Uthman says: his father had the honour of being a Companion); he narrated: The Prophet (peace and blessings be upon him) said: "Rajab is a great month in which Allah Almighty multiplies good deeds. Whoever fasts one day of Rajab, it is as though he fasted a whole year; whoever fasts seven days of it, the seven gates of Hell are closed for him; whoever fasts eight days of it, the eight gates of Paradise are opened for him; whoever fasts ten days, whatever he asks of Allah Almighty, Allah Almighty grants it to him; whoever fasts fifteen days, a caller calls out from the heaven saying: 'Your past sins have been forgiven, so begin your deeds anew.' And whoever does more (good), Allah Almighty also grants him more (reward). In the month of Rajab, Allah Almighty carried Sayyiduna Nuh (peace be upon him) in the Ark, so he fasted the month of Rajab and ordered his companions to fast as well." (Allamah al-Haythami says:) I say: After this he mentioned the full hadith; the complete report has already passed, along with the discussion of it, in the chapter on the fast of Ashura.
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الصيام / 5153
Hadith Gradingمحدثین:إسناده ضعيف جدا, قال الهيثمي:رواه الطبراني في الكبير، وفيه عثمان بن مطر الشيباني، وهو ضعيف جدا (3/188)
Hadith Takhrij«أخرجه المعجم الكبير للطبراني برقم: 5538»