3 lucky dates: Can a number "contain itself"?

3 lucky dates: Can a number "contain itself"?: "Does pi contain pi? No. If pi contained pi, at the point where the 'contained pi' started, pi would become a repeating decimal. Then pi woul..."

Can a number "contain itself"?

Does pi contain pi?
No. If pi contained pi, at the point where the "contained pi" started, pi would become a repeating decimal. Then pi would not be irrational. Hence, pi cannot contain pi.

Is there any way that a number can "contain itself" other than it having a pattern that repeats itself?


Here's another way to look at it.
If a number contained itself starting after n digits, then the first n digits would be the same as the second n digits. Similarly, the second n digits of the copy would be the same as the first n digits of the copy which means, since the second n digits of the copy are the third n digits of the original number, the third n digits of the original number would be the same as the first n digits. And so on, and so on, to infinity. The number would be a repeating decimal of period n.

3 lucky dates: Recreation math & fun with Num3ers

3 lucky dates: Recreation math & fun with Num3ers: "Semiprime: a semiprime is a number of the form p*q where p and q are primes, not necessarily distinct. http://en.wikipedia.org/wiki/Semipri..."

Recreation math & fun with Num3ers

Semiprime: a semiprime is a number of the form p*q where p and q are primes, not necessarily distinct.

http://en.wikipedia.org/wiki/Semiprime

http://mathworld.wolfram.com/Semiprime.html


For example,
842 (= 2 * 421) is a semiprime sandwiched between semiprimes: 841 and 843
841 = 29 * 29 = 29^2
843 = 3 * 281

Here's the list of the first 10,000 Primes :

http://primes.utm.edu/lists/small/10000.txt


For example, between consecutive primes 113 and 127 there are six semiprimes:
115 (=5*23), 118 (=2*59), 119 (=7*17), 121 (=11*11), 122 (=2*61), 123 (=3*41).

Could you find others?
And find a prime gap that is less and more than 6 semiprimes.

Perfect square dates

A full date number consists of a single eight-digit number sequence given by dd-mm-yy.

For example, today's date is : 15 October, 2010, so we write : 15102010

This number is not a square.

The prime factors of the number 15102010 are :  2 x 5 x 7 x 11 x 11 x 1783

The 21st century has 18 perfect square dates :

The first perfect square date of this century occurred on 9 Jan. 2004 

#1 --> 9 Jan. 2004 (09012004 = 3002 x 3002)

Then,

#2 --> 4 Jan. 2009 (04012009 = 2003 * 2003) 

#3 --> 3 May 2009 (03052009 = 1747 * 1747).

#4 --> 16 March 2016 (16032016 = 4004 * 4004).

#5 --> 1 Sept. 2025 (01092025 = 1045 * 1045).

#6 --> 27 Sept. 2025 (27092025 = 5205 * 5205).

#7 --> 1 Jan. 2036 (01012036 = 1006 * 1006) 

#8 --> 2 April 2041 (02042041 = 1425 * 1425) 

#9 --> 9 April 2049 (09042049 = 3007 * 3007) 

#10 -> 18 Dec. 2049 (18122049 = 4257 * 4257)

#11 -> 4 March 2064 (04032064 = 2008 * 2008)

#12 -> 5 Feb. 2081 (05022081 = 2241 * 2241) 

#13 -> 16 July 2081 (16072081 = 4009 * 4009)

#14 -> 2 Feb. 2084 (02022084 = 1422 * 1422)

#15 -> 2 June 2096 (02062096 = 1436 * 1436)

#16 -> 13 March 2100 (13032100 = 3610 * 3610) 

#17 -> 29 May 2100 (29052100 = 5390 * 5390)

#18 -> 26 Nov. 2100 (26112100 = 5110 * 5110)

The 20th century had 3 perfect square dates :

#1 --> 7 Jan. 1904 (07011904 = 2648 x 2648) 

#2 --> 6 March 1936 (06031936 = 2456 x 2456) 

#3 --> 19 June 1956 (19061956 = 4366 x 4366)

3 lucky dates: 3 lucky dates: 8-8-8, 9-9-9, 10-10-10

3 lucky dates: 3 lucky dates: 8-8-8, 9-9-9, 10-10-10: "Mother has 3 babies on dates 8-8-8, 9-9-9, 10-10-10 Her first was born on Aug, 8, 2008, her second on Sept. 9, 2009 and her most recent on ..."

3 lucky dates: 8-8-8, 9-9-9, 10-10-10

Mother has 3 babies on dates 8-8-8, 9-9-9, 10-10-10

Her first was born on Aug, 8, 2008, her second on Sept. 9, 2009 and her most recent on Oct. 10, 2010.

Yes, that's 8-8-08, 9-9-09 and 10-10-10.

While the dates might seem "incredibly rare," they're really not. Such a lineup can only happen in the first 12 years of the century and at least 10 months apart, says Shannon McWeeney, a professor of biostatistics at the Oregon Health Sciences University in Portland.

"Given that the first birth occurred in that window, the probability is not as astronomical as you might be compelled to think," she says.In fact, it's not that high a number at all, says Philip Stark, a professor of statistics at the University of California, Berkeley. "The 'chance' you get depends on the assumptions you make," he says. One set of assumptions gives a chance of about 1 in 50 million. More realistic assumptions — including allowing at least 11 months between births — increases it to about 1 in 2,500. Since thousands of women in the United States had kids in 2008, 2009 and 2010, this suddenly seems a little less extraordinary. But humans "like to look for patterns, to make sense of things" he says.For the Sopers, three is simply their lucky number — "we don't have any more planned," says Barbara.

Source:

 http://www.usatoday.com/yourlife/parenting-family/babies/2010-10-14-Birthday14_ST_N.htm

Her first was born on Aug, 8, 2008 ... 8 Aug. 2008 ---> 080808

her second on Sept. 9, 2009 and ...... 9 Sept. 2009 --> 090909 

her most recent on Oct. 10, 2010...... 10 Oct. 2010 --> 101010

or we write:

08082008, 09092009 and 10102010

The factors of 8082008 are: 1  2  4  8  11  22  44  88  91841  183682  367364  734728  1010251  2020502  4041004  8082008 

The prime factors are:  2 x 2 x 2 x 11 x 91841

The factors of 9092009 are: 1  47  193447  9092009  

The prime factors are:  47 x 193447

The factors of 10102010 are: 1  2  5  10  1010201  2020402  5051005  10102010  

The prime factors are:  2 x 5 x 1010201

[to be continued]