There's a mistake in your question. But I'm going to write this assuming your question is correct. See the very end of my answer for an important point.
Whether you're "special" depends on your definition of special, I guess. It does put you in a fairly rare class of dates.
Let's look at the likelihood of having a birthdate that matches your conditions.
1) The year of your birth is a prime number.
2) The month of your birth is a prime number.
3) The day-of-the-month of your birth is a prime number.
In the past 100 years, there were only 13 years that were prime: 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, and 2003.
In any given year, there are only five months that are prime: 2, 3, 5, 7, and 11.
And in a given month, there are only eleven possible days that are prime, though not all of these occur in every month: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
Let's calculate how many total days there were in the past 100 years, and how many of those dates meet your criteria.
First, we'll calculate the total number of days in the past 100 years, ignoring leap years (we'll add those in later). Every year has 365 days, so 365 times 100 equals 36,500.
Now, let's add in the leap years. Leap years come every 4 years, except that if a year is divisible by 100, it's not a leap year. Except if it's divisble by 400, it is a leap year. The only "exceptional" year in the past 100 years is the year 2000, and that's divisible by 400, so it was a leap year. So there were twenty-five leap years over the past 100 years (the period from April 22, 1906 through April 21, 2006).
So the total number of days in the past 100 years is 36,525.
Now, how many of those dates fit your criteria?
In a non-leap year, there are 52 dates that fit your criteria. All leap years are divisible by four, and thus they are not prime numbers, so we can completely ignore leap years in this calculation. The dates are:
February 2, 3, 5, 7, 9, 11, 13, 17, 19, 23
March 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31
May 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31
July 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31
November 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29
Add them up, and you'll see there are 52 of them. 52 dates per year, multiplied by thirteen years that are prime comes out to 676.
So out of 36,525 dates someone might have been born in the past 100 years, only 676 of them meet your criteria. That's about 1.85% of them.
So, if we assume that the odds of being born on any given date is about equal (not true) and that a given person is a random age between 0 and 100 (also not true), they have about a 1.85% chance of meeting your criteria.
HOWEVER, and here we get to the mistake in your question, you were not born on a date with all prime numbers. 1957 is not a prime number; its factors are 19 and 103 (19 * 103 = 1957).
So it turns out you're not special at all. You're just normal, like the rest of us. :)