Prime numbers lie at the core of some of the oldest and most perplexing questions in mathematics. Evenly divisible only by themselves and 1, they are the building blocks of integers. In recent decades, prime numbers have emerged from their starring roles in mathematical research (SN: 5/25/02, p. 324: Available to subscribers at Prime Effort: Powerful conjecture may be proved) by becoming prized commodities–as elements in a cryptographic scheme widely used to keep digital messages secret (SN: 2/6/99, p. 95).
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Although there are infinitely many primes, they are also relatively scarce and rather haphazardly scattered among the integers. Indeed, of the first 25 billion whole numbers, only 1,091,987,405–or about 4 percent–are primes, and the proportion of primes decreases as the numbers get bigger.