Did Richert actually show it? I don't read it that way. Rather, only that it was possible to show it. So who, if anyone, since 1951 *has* shown it?
I'm still struggling with this. On a purely mechanical level though I think I understand now how Richert showed "that the number n of digits of the absolute prime number Bn(a,b) is divisible by 321653308662329838581993760": In[1]:= LCM[16,18,22,28,46,58,60,96,166,178,262,382,502,862,886,982] Out[1]= 321653308662329838581993760 The numbers on which we are doing the LCM are one less than a number of primes whose PrimitiveRoot[{primes},9] are all 10. Why didn't Richert didn't use all the primes (greater than 16, otherwise < https://oeis.org/A001913 >) less than 1000 that yield the result? I guess that in 1951 it was tedious work: In[2]:= t={};Do[If[PrimitiveRoot[Prime[i],9]==10,AppendTo[t,Prime[i]]],{i,PrimePi[1000]}];t Out[2]= {17,19,23,29,47,59,61,97,109,113,131,149,167,179,181,193,223,229,233,257,263,269,313,337,367,379,383,389,419,433,461,487,491,499,503,509,541,571,577,593,619,647,659,701,709,727,743,811,821,823,857,863,887,937,941,953,971,977,983} In[3]:= LCM[16,18,22,28,46,58,60,96,108,112,130,148,166,178,180,192,222,228,232,256,262,268,312,336,366,378,382,388,418,432,460,486,490,498,502,508,540,570,576,592,618,646,658,700,708,726,742,810,820,822,856,862,886,936,940,952,970,976,982] Out[3]= 1903624829738325512638755460871681762868757605195485779200 It's now just a simple matter to scale to the "primes and their primitive roots up to 10^5": In[4]:= t={};Do[If[PrimitiveRoot[Prime[i],9]==10,AppendTo[t,Prime[i]]],{i,PrimePi[10^5]}];t Out[4]= {17,19,23,29,47,...,99901,99971,99989} In[5]:= LCM[16,18,22,28,46,...,99900,99970,99988] Out[5]= 6284645765...5616000000 ~6*10^4044 which is different from Richert's suggested 6*10^175 (perhaps) for the same reason that my 1903624829738325512638755460871681762868757605195485779200 (above) is different from his 321653308662329838581993760. At any rate, doesn't (then) the suggestion that all the elements of A003459 past 991 being repunits boil down to there being an infinite number of terms in A001913?