1) MATHEMATICALLY COMMENSURABLE PRAYERS?
Hadith: The salat (ritual prayer) performed in congregations is 27 times superior to the salat performed individually.
Bukhari Ezan, Muslim Mescid, Muvatta Jamaat
You may consider this hadith not in contradiction with the Quran, nor in conflict with another hadith or is in any way illogical; yet you may be sure that it is a contrived hadith,for there is no such information in the Quran. There are also hadiths that say that the salat performed after having performed one’s ablutions using the miswak (stick of wood beaten into fibers at one end and used as a toothbrush) is twenty-seven times or seventy times superior to the salat performed with ablutions performed with one’s turban on.