Number Patterns

Numbers form beautiful patterns in relation to other numbers. Students can be given the first few statements in a pattern. Using logic, they can write a few more steps. They can also verify the truth of these statements by actual calculations.

Here are a few patterns. The Internet can yield many more such patterns.

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321

Sum of any sequence of odd numbers, starting with 1 will always be a square.

The square of the sum of some numbers starting with 1 will be equal to the cubes of the individual numbers,

(1 + 2 + 3 + 4 )2 = 13 + 23 + 33 + 43

Numbers & their Products

9*9= 81 and 8+1 = 9

45*45= 2025 and 20 +25 = 45

55*55 = 3025 and 30 +25 = 55

99*99= 9801 and 98+01 = 99

703*703= 494209 and 494+209= 703

5292*5292 = 28005264 and 28+ 005264 = 5292

1713 + 2377 + 1464 = 5554 & 5554^3 = 171323771464

An Interesting Prime Number

If you write the numbers from 82 to 1 in descending order, you will get a 155-digit prime number.

8281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827262524232212019181716151413121110987654321 is a prime!