Milo, read the Rhind Mathematical Papyrus as written and don't phantasize about the methods Ahmes used, study the methods he actually used. And, by the way, the topic of this thread are the prime numbers and pi. If you wish you can start a new thread on RMP 66; here I won't discuss it anymore, nor another problem of the RMP.
'3 minus '3x5 '3 minus '4x7 '3x17 '3 minus '4x7 '10x13 '3x29 '3 minus '4x7 '10x13 '16x19 '3x41 '3 minus '4x7 '10x13 '16x19 '22x25 '3x53 '3 minus '4x7 '10x13 '16x19 '22x25 '28x31 '3x65
I am still wondering about this series. The value of the series, approximated by the complementary stairways, is 0.27854..., probably 0.278548... Can this number play a role in prime theory? I asked this question before. Now I see all odd primes appear in the approximating stairways when I write them in the above form, and so I will study their arrangement - is their pattern of any meaning?