Egyptian 2/D Table (D Prime Number): An Entirely New Analysis Consistent with the Idea of a Progressive Teamwork

For h=3 or 4, Egyptian decompositions into h unit fractions, like 2/D = 1 / D1 +... +1 / Dh, were given by using ( h-1) divisors ( di) of D1. This ancient modus operandi, well recognized today, provides Di=DD1/di for i greater than 1. Decompositions selected (depending on di) have generally been studied by modern researchers through the intrinsic features of d i itself. An unconventional method is presented here without considering the di properties but just the differences dh-1- dh. In contrast to widespread ideas about the last denominator like ‘Dh smaller than 1000’, it is more appropriate to adopt a global boundary of the form ‘Dh smaller or equal to 10D’, where 10 comes from the Egyptian decimal system. Singular case 2/53 (with 15 instead of 10) is explained. The number of preliminary alternatives before the final decisions is found to be so low (71) for h=3 or 4 that a detailed overview was possible in the past. A simple additive method of trials, independent of any context, can be carried out, namely 2n+1= d2 +... + dh. Clearly the decisions fit with a minimal value of the differences dh-1- dh, independently of any di values.