According to the International Standard Organisation's ISO 8601, week 1 of any year is the week including 4 January.
It is a curious consequence of the rules underlying the Gregorian calendar that the thirteenth of the month is more likely to fall on a Friday than any other day of the week. Here is the reason:
The Gregorian calendar operates on a 400-year cycle with a Leap Day added every fourth year, except for three out of every four century years. That results in exactly 146,097 days every 400 years. But 146,097 = 7 x 20,871. In other words, 400 years comprise exactly 20,871 weeks. So, whatever the date is, you can be sure that date will fall on the same day of the week in 400 years' time. Since there are 4,800 months in 400 years, there will be 4,800 thirteenths of the month, and whatever days of the week they fall on will be repeated during all subsequent 400-year cycles. Since 4,800 is not divisible by seven, the thirteenths cannot be equally divided among the seven days of the week. When you work it out, it turns out that every 400 years, there are 685 Monday the thirteenths, 685 Tuesday the thirteenths, 687 Wednesday the thirteenths, 684 Thursday the thirteenths, 688 Friday the thirteenths, 684 Saturday the thirteenths and 687 Sunday the thirteenths.