Today we had nothing planned, so we went to Sea life here in Kansas City. If you haven't been, It's an awesome aquarium with consistently unique and spotless tanks, with interesting sea creatures to look at. I'm especially fond of the huge rays, but the sharks and the sea turtle are pretty cool too. The best part is several places throughout the building you can walk under the aquarium as the creatures in the large tank swim over you. And it turns out that with a Friends of the Kansas City Zoo pass you can get a huge discount.
After Sea life, we hit grabbed a snack on took in the children's play area at Crown Center. Julianne and I decided that someone had a dream job designing and building this thing. This one was based on favorite childhood stories and was really imaginative and engaging for the kiddos.
After that we went to the Wonderscope Children's museum (also in Crown Center). The kids get to run around creating with a really well supplied area of markers, die cut paper, and tape. It was cool to get to make our own puzzle on a board decorated by the boys, make a custom keep sake box, water color some glossy paper and dry it in what looked like a modified pizza oven.
After all that excitement we took it easy the rest of the day, and by take it easy I mean started thinking about prime numbers again. Prime numbers trigger something strange in my mind. It's a feeling like there should be some devilishly simple way of predicting them, but every attempt to do so is thwarted. So it's that interesting puzzle that is fun to think about.
The same goes for prime factorization of semiprime numbers, that is more simply put: figure out what two prime numbers we multiplies together to get this number. RSA put out a challenge years ago to factor some of these numbers. I've been working on RSA-1024 for all of an hour now, so I can tell you definitively, This number's prime factors are (...3 * ...1) or (...7 * ...9) since as we know when you multiply big numbers, only the last digit has any effect on the last digit of the result. we also know that the numbers at the end must be 1,3,7 or 9 because anything even greater than 2 is not prime because it is then divisible by 2, and anything ending in 0 or 5 that is greater than 5 is also not prime because it is then divisible by 5. An interesting thing I've found is the the only possible prime ending numbers also are the only ones that exhibit the behavior of having the whole set of numbers contained in the last digit of the result of that number multiplied by all other numbers[1]. Or said another way, if you take the last digit from the result of 3 * [1-9] all of the numbers 1-9 come up, and the same for 1, 7 and 9. But no other numbers. I also know that adding the digits of the prime factors there will be 1023-1024 total digits and we can guess that it's likely more in the middle of the range and not a 2 digit number * a 1021 digit number.
knowing these two things, if both primes are already known we should be able to just look them up and guess at which ones they might be from this list, [2] but to be fair it's an awfully big list. I think it may be possible to branch out the initial known endings of 1-3 or 7-9 into the last two digit combinations and that should help narrow things down considerably.
[1]
0 1 2 3 4 5 6 7 8 9
----------------------------
1| 1 2 3 4 5 6 7 8 9
2| 2 4 6 8 0 2 4 6 8
3| 3 6 9 2 5 8 1 4 7
4| 4 8 2 6 0 4 8 2 4
5| 5 0 5 0 5 0 5 0 5
6| 6 2 8 4 0 6 2 8 4
7| 7 4 1 8 5 2 9 6 3
8| 8 6 4 2 0 8 6 4 2
9| 9 8 7 6 5 4 3 2 1
[2]
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