Maximum Length Decimals

Extract

In his talk on Decimals at the Annual General Meeting of the Mathematical Association, 1962, (see the Mathematical Gazette, XLVII, 1963, p. 25), Mr. Green observed that the recurring decimal expression for 1/p where p was a prime other than 2 or 5 had the maximum possible length of p – 1 if and only if 10 was a primitive root of the modulus p. In practice there was maximum length for

p = 17, 19, 23, 29, 47, 59, 61, 97

but not for

p = 13, 31, 37, 41, 43, 53, 67, 71, 73, 79, 83, 89,

and he did not see any reason or pattern behind these figures.