This is the 13th page. 13 is an unlucky number. Of course I am not superstitious. But this still is the 13th page.
Problem is that the product of two numbers seems just as long as the two numbers written one after the other.
For numbers like 10, 100, 1000, 10,000 and so on, this is obvious, e.g.:
1000 (3 zeros) * 100,000 (5 zeros) = 100,000,000 (3 + 5 = 8 zeros).
Because of the 1's in front and the * sign, the prime product (left side of equation) when written out is two figures longer than the single number of its outcome (right side of equation).
The fact that this holds for all powers-of-ten numbers suggests that it also holds for all numbers between the powers-of-ten numbers.
It clearly holds for some known prime products too.
1.
RSA-130
=
18070 82088 68740 48059 51656 16440 59055 66278 10251 67594 01349 17012 70214 50056 66254 02440 48387 34112 75908 12303 37178 18879 66563 18201 32148 80557
(number of 130 figures)
=
45534 49864 67359 72188 40368 68972 74408 86435 63012 63205 06960 09990 44599
(prime number of 65 figures)
*
39685 99945 95975 54290 16112 61628 83786 06757 64491 12810 06483 25551 57243
(prime number of 65 figures)
2.
((12^166) + 1) / 13 (prime number of 180 figures)
=
78853 91524 79959 92358 34738 70729 72515 87966 47538 88371 88632 62181 41334 73912 36469
(prime number of 75 figures)
*
16311 78452 56502 92068 75585 43656 69702 02474 11364 46212 03858 93160 94580 45532 50187 47260 47433 26476 43552 26803 78897
(prime number of 105 figures)
3.
RSA-155 =
10941 73864 15705 27421 80970 73220 40357 61200 37329 45449 20599 09138 42131 47634 99842 88934 78471 79972 57891 26733 24976 25752 89978 18337 97076 53724 40271 46743 53159 33543 33897
(number of 155 figures)
=
10263 95928 29741 10577 20541 96573 99167 59007 16567 80803 80668 03341 93352 17907 11307 779
(number of 78 figures)
*
10660 34883 80168 45482 09272 20360 01287 86792 07958 57598 92915 22270 60823 71930 62808 643
(number of 78 figures)
78 + 78 = 155 + 1, so if the numbers are right, the prime product when written out in its factors is one figure longer than the outcome prime product. And that is excluded the * multiplication sign.
It seems the number of figures in the outcome of a multiplication is always equal to or a little SHORTER than the total number of figures in the written out prime product. But I cannot really prove it.
Frits talked about sum-of-the-products-of-primenumbers. Products of primes don't change the number of figures needed, and that is excluded the 1's in front and the * signs. However, written out sums enlarge the number of figures severely. 29576779 (8 figures) + 4492 (4 figures) = 295812719 (8 figures), so here are 8 + 4 = 12 figures at the left side and only 8 figures at the right side of the equation. The sum-of-the-products-of-primenumbers when written out, is much longer than its calculated outcome.
But as said, I cannot prove this completely.