Hi there, here’s a whole new subject for you to ponder here.
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Mathematically 2024 is a unique year because it has more instances of the day multiplied by the month equaling the year than any other year. So for 2024 the dates are 1.24, 2.12, 3.8, 4.6, 6.4, 8.3, 12.2 or 7 instances. No other year has more than five such occurrences so cherish 2024’s #1 standing, it will be a century until this happens again!
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Learning to do math in your head is a skill that comes in handy and can be much quicker than digging up your calculator function on your phone or computer. It’s not that hard, let’s start with the multiplication tables that you memorized back in elementary school and even extend them past 1-10 to 1-12. The elevens are easy: 1x11=11, 2x11=22, 3x11=33 and so on to 11x11+121 and 11x12=132.
The 12s are almost that easy, 1x12=12, 2x12=24, 3x12=36, 4x12=48, note the first number goes up by 1, the 2nd by 2. We’ve done 11x12=132, so 12x12=144.
And here’s a trick for multiplying numbers in your head, let’s say 52x36. Double one and divide one by half, so 104x18 or 26x72, keep going so 208x9 or 13x144 and you’ll find both equal 1,872. Odd numbers are trickier but if you remember decimal points, you’ll be able to nail those also. 17x15=34x7.5 or 30x8.5,either way comes to 255. Larger numbers are more difficult but the same technique does work, let’s look at 87x39 as an example. 174x19.5 or 43.5x78, keep going 348x9.75 or 21.75 x 156, 696x4.875 or 10.875x312 and that can be figured by multiplying 312x1=3120 and then 312 x 7/8 for 273 more and voila, you reach the correct answer of 3,393!
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Now let’s look at squares and a nifty trick to figure them. We’ll start with 10x10=100, 11x11=121, 12x12=144, 13x13=144+25=169, 14x14=169+27=196 and so on.
Notice that if you add up the two numbers and add 1, it will equal the next number’s square. 20x20=400 so 21x21= 20+20+1=441. 100x100=10,000 so 101x101=100+100 +1=201 added to the 10,000 to total 10,201. And so on, ad infinitum.
Speaking of infinity, now let’s have a look at prime numbers, numbers greater than 1 that only have two factors, 1 and the number itself.If you divide a prime number by a number other than 1 and itself, you will get a non-zero remainder.
That said, let’s see what prime numbers there are between 2 and 100.
First off, except 2, even numbers can never be prime numbers as they are divisible by two and themselves. All numbers ending in 5 also don’t make the grade as each is divisible by 1 and 5.
So here are the primes in the first 100: 2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97
Now, you’d think that eventually there would be no prime numbers after a certain point as we venture into 4, 5, 6 and more digit numbers.
But no, it seems that no matter how big the number, a new prime will come along, thus prime numbers are infinite, the largest found to date is
T 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10.Thanks to Patrick Laroche and Wikipedia for this information. According to Euclid, who created the theorem, prime numbers are infinite so there would not seem to be much point in exploring further to
Wikipedia of course has plenty about primes so for more, here’s that link:
And, for those desiring even more information about prime num bers, here’s a link to the GIMPS site, standing for the Great Internet Mersenne Prime Search.
Of course, if you can come up with an even bigger prime, kindly let them know. Happy hunting!