Problems & Puzzles: Puzzles Puzzle 208. Happy new Year 2003! Better late than never. Please all of you have my very best wishes for a new prime year (2003) like this we are just starting. Now, is there a better way of celebrating it, than posing some interesting puzzles about this prime number? I will start with one puzzling question; you are invited not only to solve it but to send other interesting questions about this prime number, OK?
Solution: Solutions came from Johann Wiesenbauer, Phil Carmody and J. K. Andersen. All of them provided the same solution: the prime number 2231588810593399. Other interesting questions related to the prime 2003 became from Johann Wiesenbauer and Jon Wharf. See below.
*** Wiesenbauer obtained it factoring 10^20031 using a " a small ECMprogram written in DERIVE 5". *** Carmody simply wrote "probably found by Harvey Dubner, but I'm not sure.". *** J.K. Andersen wrote "found in 1 minute with Michael Scott's factor.exe (modified to allow larger numbers)". He also reported that Carmody wrote to the primenumbers list "that the factor 2231588810593399 was known and is in the file http://groups.yahoo.com/group/primenumbers/files/Factors/Base10.zip" *** So two of our readers rediscovered a number that was already produced by Harvey Dubner (for other purposes?) *** Regarding the follow up questions about 2003 we have: Johan Wiesenbauer asks: (1997, 1999, 2003) is a socalled prime triple of the form (p,p+2,p+6). The one before had been (1871, 1873, 1877) and the next one will be (2081, 2083, 2087). If you look at the "distances" 126 and 84, respectively, between the triples, are they considered to be "large" or "small" when compared with an expected value obtained by heuristic reasoning? Jon Wharf asks: What is the largest
set of primes such that the average of the whole set is *** J. K. Andersen sent (3/2/03)the following followup puzzle about 2003:
*** Faride Firoozbakht wrote (May 2003):
Later (August, 2003) she added:
Another property singular for the prime 2003, sent by Faride is the following one:
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