如果R是(p^p-1)/(p-1),其中p==1(mod 4)且p>5,则R的左Aurifeullian因子的近似值为(1/e)*sqrt(R/(1+z)),其中z=
2/(3p)+28/(45p^2)+1706/(2835p^3),如果p=1.79109121151或169(210版),
2/(3p)+28/(45p^2)+86/(2835p^3),如果p=19,31,61139181或199(210版),
2/(3p)-8/(45p^2)+194/(2835p^3),如果p=37,43,67127163或193(210版),
2/(3p)-8/(45p^2)-1426/(2835p^3),如果p=13,73,97103157或187(210版),
-2/(3p)-8/(45p^2)+1426/(2835p^3),如果p=23,5310711337或197(210版),
-2/(3p)-8/(45p^2)-194/(2835p^3),如果p=17,47,83143167或173(210版),
-2/(3p)+28/(45p^2)-86/(2835p^3),如果p=11,29,71149179或191(210版),
-2/(3p)+28/(45p^2)-1706/(2835p^3),如果p=41,59,89101131或209(210版)。