Strong law of small numbers

In mathematics, the "strong law of small numbers" is the humorous law that proclaims, in the words of Richard K. Guy :
In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Earlier this "law" was reported by Martin Gardner. Guy's subsequent 1988 paper of the same title gives numerous examples in support of this thesis.

Second strong law of small numbers

file:circle_division_by_chords.svg|thumb|Guy gives Moser's circle problem as an example. The number of and. The first five terms for the number of regions follow a simple sequence, broken by the sixth term.
Guy also formulated a second strong law of small numbers:
Guy explains this latter law by the way of examples: he cites numerous sequences for which observing the first few members may lead to a wrong guess about the generating formula or law for the sequence. Many of the examples are the observations of other mathematicians.
One example Guy gives is the conjecture that is prime—in fact, a Mersenne prime—when is prime; but this conjecture, while true for = 2, 3, 5 and 7, fails for = 11.
Another relates to the prime number race: primes congruent to 3 modulo 4 appear to be more numerous than those congruent to 1; however this is false, and first ceases being true at 26861.
A geometric example concerns Moser's circle problem, which appears to have the solution of for points, but this pattern breaks at and above.