July 29 is the 210th day of the Gregorian calendar for a non-leap year (next year it will be the 211th day), so there are only 155 days remaining (and only 148 until Christmas). That makes it an interesting numerical day.

210 is an interesting number (of course it is easy to prove there are no un-interesting numbers), its the product of all the one digit primes, 2(3)(5)(7). It is also the sum of eight consecutive primes, 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41. July 29 th on a leap year, or July 30th on a non leap year, fall on the 211th day, which is a prime number. If you want to look forward to a truly PRIME day, the 219th day of the year, August 7th. It is the sum of the first 12 primes, and is the midpoint of summer in the northern hemisphere.

Numbers that are the product of all the primes from 2 to the nth prime are called "primorial", generalized from the word "factorial" for the product of consecutive positive integers. The primorials are 2, 6, 30, 210, 2310.. so 210 is the fourth primorial. It is the only primorial day that is not in January and the lastof the calendar year.

The last day that was the sum of eight consecutive primes was the 180th day of the year, June 29, and the next one will be the 240th day, August 27th, and the next one is 30 days after that, but don't expect that pattern to continue.

210 is also a triangular number, the sum of the first twenty counting numbers (1+2+3+...+ 20) . The last one before today was on July 9th. The next one will be on .. oh you can figure that out. Triangular numbers are formed by adding up the first n consecutive positive integers; and the first few are 1, 3, 6, 10,

210 is also a pronic number, 14x15, which makes it twice a triangular number also. Pronic numbers are also called rectangular numbers, and are the product of a number times one more than itself (n)(n+1). Can you find the first five numbers that are both triangular and pronic? Start with 6 (1+2+3 and 2x3) and then ??? have fun.

210 is the sum of "prime cousins", prime numbers that are seperated by four. Prime twins are numbers that are seperated by two (3 and 5, 11 and 13, 17 and 19, etc). The "prime cousins" that sum to 210 are 103 and 107. It has been two days since the last day that was the sum of "sexy primes" (primes which differ by six, 13 and 19, 31 and 37, or in this case, 101 and 107 = 208 for July 27). It will also be two days until the next one, 103 + 109 =212 for July 31.

If you wandered along the digital approximation of pi looking for 210, you would have to go a long way to find it. The string first appears beginning with the 1,317th decimal digit of pi (02898915 210 475216205696). For comparison, Feynman's Point, the first occurance of six consecutive digits ,in this case 999999, begins at only the 762nd decimal place . The next string of six consecutive anythings happens to be six more nines that begins at the 193,024th decimal place. I hear you wondering, and 666 does occur, but not until the 2,440th decimal place. The first three digit repunit to appear is 111, which appears at the 153rd decimal place.



I think it is also curious that the binomial representation is 11010010, since it is 110 + 100 in base 10.