Template:Sequence of the Day for September 22

Intended for: September 22, 2012

Timetable

• First draft entered by Frank Ellerman on September 22, 2011 ✓
• Draft reviewed by Charles Greathouse on September 23, 2011 ✓
• Draft approved by Alonso del Arte on April 1, 2012 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A079614: Bertrand’s constant.

1.251647597790463...

Bertrand’s postulate shows that for each

n > 3

there is at least one prime

n < p < 2 n  −  2

. Likewise for

n > 1

there is at least one prime

n < p < 2 n

. Therefore a constant

b

exists where

⌊  2 b⌋ , ⌊  2 2 b⌋ , …, ⌊  2 2  ⋰ 2 b⌋ , …

are all primes (cf. A051501). Finding more digits for

b

requires finding better bounds for the prime counting function.