Sorry, a little of topic...
The recent heroes in this field are H J J te Riele, who "knows
everything about amicable numbers" according to a now forgotten usenet
poster and Lee and Madachy, who published "The history and discovery of
Amicable Numbers" in the Journal of Recreational Mathematics in 1972,
Your list of heroes are far out of date. Here are some recent heroes:
- Herman te Riele: still knowing (almost) everything about amicable pairs.
- Stefan Battiato&Walter Borho: early mass production of pairs (30,000+),
first pair with members coprime to 6.
- Holger Wiethaus: the first pair with over 1000 digits (and producing 10,000+
pairs).
- Derek Ball: independent mass production and still very active.
- Frank Zweers: many pairs with 1000+ digits.
- Mariano Garcia: 80+ years old, still very active, holds record with
a 5577 digit pair found in 1997.
- Yasutoshi Kohmoto: first pair with members coprime to 30.
- David Moews&Paul Moews: all pairs < 3*10^11 using a sieve algorithm.
- David Einstein: nearly all pairs < 10^13 using a tree algorithm.
- Patrick Costello: methods for type (n,1) pairs and still very active.
There are far more amicable pairs known than even perfect numbers, yet
Guy's claim on their infinite number or otherwise is, surprisingly,
weaker. "It is not known if there are infinitely many, but it is
believed that there are."
Please visit http://www.vejlehs.dk/staff/jmp/aliquot/knwnap.htm
for a list of 550,000+ amicable pairs. My database is growing with
around 50,000-100,000 pairs every year, so, yes without any doubt
there is an infinite number of amicable pairs.
Best wishes
Jan
