Prime Curios!: 209

209
(another Prime Pages' Curiosity)

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The curve 42x² - y² = 209 contains the 'prime points' (3, 13), (5, 29), (7, 43), and (13, 83). [Buddenhagen]

209 = 11 x 19 is a member of a series n(n + 1) - 1 with the property that all terms greater than 1 are divisible by primes of form 10k + 1 or 10k - 1, but not 10k + 3 or 10k - 3. There is an infinity of pairs x,y where x² - y² - xy = 209 for x, y integer. [McNamara]

The smallest composite primorial - 1.

The number of consecutive composite numbers that follow the prime 20831323, the first prime gap exceeding 200.

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