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.
Some interesting examples can be seen here.
Because relatively few Mersenne primes are known, people often conjecture about patterns.