Project 1: Factorization of First Holes

My primary object is to provide complete listings of the factorizations up to the highest completely factorized exponent for bases 2 to 999. Other listings (in print and on the Net) omit one or more of the following:

• Factors less than 5 digits
  
• Factors less than 10 digits
  
• Algebraic factors
  
• Aurifeuillian factors
  
• Factors of even exponents
  
• Bases that are perfect powers
  
• Largest factors
  

My secondary object is to try to help complete the factorizations for exponents up to 50. My contribution to this is minor: of 28,076 non-trivial factors in my database, I claim to have discovered only 1,106 (3.94%) of them.