Abu Huraira reported God’s Messenger as saying, “The five [daily] prayers, Friday to Friday and Ramadan to Ramadan make atonement for what has happened since the previous one when major sins have been avoided.” Muslim transmitted it.
Hadith Referenceمشكوة المصابيح / كتاب الصلاة / 564
Hadith Gradingالألبانی:صَحِيحٌ | زبیر علی زئی:صحيح
Hadith Takhrij´تحقيق و تخريج: محدث العصر حافظ زبير على زئي رحمه الله` «رواه مسلم (16/ 233)»