Strong law of small numbers

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More properly known as Guy's Strong Law of Small Numbers. In 1988 mathematician Richard K. Guy published a paper "The Strong Law of Small Numbers". In it he states,

"There aren't enough small numbers to meet the many demands made of them."

Just because a pattern holds for all the numbers that you have checked so far, it does not mean it will for all numbers. Double Mersenne numbers are a good example of this. The first 4 terms yield primes, but factors for next four terms have been found (after a gap of over 80 years after M12 was proven prime). Many believe that the Catalan Sequence is also a case of this law, since only a few element can be tested.

Chris Caldwell has an excellent page on this here.

Some interesting examples can be seen here.

Because relatively few Mersenne primes are known, people often conjecture about patterns.

External links