explanation is known or expected to exist (as is the case for most others here). It is a consequence of the fact that 163 is a Heegner number. There are several integers () such that for some integer n, or equivalently for the same These are not strictly coincidental because they are related to both Ramanujan's constant above and the Heegner numbers. For example, so these integers k are near-squares or near-cubes and note the consistent forms for n = 18, 22, 37, with the last accurate to 14 or 15 decimal places. is almost an integer, to about 8th decimal place. Other numerical curiosities . In a discussion of the birthday problem, the number occurs, which is "amusingly" equal to to 4 digits. , the product of three Mersenne primes. , the geometric mean of the first 6 natural numbers, is approximately 2.99; that is, . Decimal coincidences , making 3435 the only non-trivial Münchhausen number in base 10 (excluding 0 and 1). If one adopts the convention that , however, then 438579088 is another Münchhausen number. and are the only non-trivial factorions in base 10 (excluding 1 and 2). , , , and . If the end result of these four anomalous cancellations are multiplied, their product reduces to exactly 1/100. , , and . (Along a similar vein, .) , making 127 the smallest nice Friedman number. A similar example is . , , , and are all narcissistic numbers. , a prime number. The fraction 1/17 also produces 0.05882353 when rounded to 8 digits. . The largest number with this pattern is . . This is equivalent to , , which is close to . Also, , which is even closer to . . Numerical coincidences in numbers from the physical world Speed of light The speed of light is (by definition) exactly 299,792,458 m/s, extremely close to 3.0 × 108 m/s (300,000,000 m/s). This is a pure coincidence, as the meter was originally defined as 1/10,000,000 of the distance between the Earth's pole and equator along the surface at sea level, and the Earth's circumference just happens to be about 2/15 of a light-second. It is also roughly equal to one foot per nanosecond (the actual number is 0.9836 ft/ns). Angular diameters of the Sun and the Moon As seen from Earth, the angular diameter of the Sun varies between 31′27″ and 32′32″, while that