First strong law of small numbers

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

— Richard K. Guy

The first strong law of small numbers is known as the strong law of small numbers.

This law is a warning against drawing conclusions based on the observation of a few small numbers. For example, a quarter of the first hundred positive integers are prime numbers, whereas the formula $\scriptstyle {\frac {100}{\log 100}}\,$ suggests only 21 or 22 are primes; of the first ten million, 664579 are prime but the formula suggests only 620420 or 620421 are prime: even some of the greatest minds of the 19 th century were misled away from the prime number theorem as they tried various adjustments to the formula, unaware that for large enough numbers, the adjustment is unnecessary.

See also

• Second strong law of small numbers
• Pigeonhole principle
• Frivolous theorem of arithmetic

External links

• Richard K. Guy, The Strong Law of Small Numbers.
• Richard K. Guy, The Second Strong Law of Small Numbers.