Those Fascinating Numbers
1
the only number which divides all the others.
2
the only even prime number.
3
the prime number which appears the most often as the second prime factor of
an integer, and actually with a frequency of
1
6
(see the number 199 for the list
of those prime numbers which appear the most often as the
kth
prime factor of
an integer, for any fixed k 1).
the smallest Mersenne prime (3 =
22
−1): a prime number is called a Mersenne
prime if it is of the form
2p
1, where p is prime (see the number 131 071 for
the list of all Mersenne primes known as of May 2009);
the prime number which appears the most often as the second largest prime
factor of an integer, that is approximately (1 + log 2 + 3
2
log 3)x/ log x times
amongst the positive integers n x (see J.M. De Koninck [44]);
the smallest triangular number 1: a number n is said to be triangular if there
exists a number k such that
n = 1 + 2 + 3 + . . . + k =
k(k + 1)
2




.
.
.
1
http://dx.doi.org/10.1090/mbk/064/01
Previous Page Next Page