# Vivaldi's favorite

I am looking for a single word, that is missing. Everything you need to know, is right here:

953762581590 126971489190
2391402      2363595
158960430265 4657255395
3639090      126971489190

126971489190 3189841410
3627756834   27034799610
13949845     8558914
27034799610  138639998

126971489190 1802319974
6350162      66685839038
95252430     228777458
2051102326   83699070


But, I believe a nudge in the right direction is nice. That's why I have included the following image: The word is

WINTER.

Part 1:

Let's enlarge the image a bit: This is a rebus. Φ is the Greek letter PHI, but "H = R", so PHI becomes PRI.
Ω is the Greek letter OMEGA, but instead of G we have "G-1". Taking A = 1 (so that Z = 26), G-1 = 7-1 = 6 = F. So OMEGA becomes OMEFA. But we have to subtract the O too, as suggested by "-O". So we have MEFA.
Finally we have C → RS. "→" could mean "to", so we get C TO RS, or CTORS, as a result.

All in all, we have PRI + MEFA + CTORS, which with the right spacing becomes PRIME FACTORS.

So perhaps we need to take the prime factors of the listed numbers?

Part 2:

Let's try arranging the numbers and their respective prime factors in a table, where the former are row labels and the latter are column labels. Let's also denote which primes are prime factors of the given number with an "O".
Also importantly, we read each grouping of eight numbers top to bottom then left to right. Only then do we move to the next grouping.

Doing this gives us the following table:

                  02 03 05 07 11 13 17 19 23 29 31 37 41 43
953762581590   O  O  O  O     O  O  O  O     O  O  O
2391402   O  O           O        O     O        O
158960430265         O  O     O  O  O  O     O  O  O
3639090   O  O  O  O     O              O        O

126971489190   O  O  O  O     O        O     O  O  O  O
2363595      O  O        O  O     O     O
4657255395      O  O        O     O  O     O     O  O
126971489190   O  O  O  O     O        O     O  O  O  O

126971489190   O  O  O  O     O        O     O  O  O  O
3627756834   O  O           O        O     O  O  O  O
13949845         O  O     O        O     O        O
27034799610   O  O  O  O     O  O  O  O     O        O

3189841410   O  O  O  O        O  O        O  O  O
27034799610   O  O  O  O     O  O  O  O     O        O
8558914   O        O     O              O  O  O
138639998   O        O        O  O  O     O        O

126971489190   O  O  O  O     O        O     O  O  O  O
6350162   O        O     O        O        O  O
95252430   O  O  O  O     O        O        O  O
2051102326   O        O     O  O  O  O        O  O

1802319974   O        O     O  O  O  O     O        O
66685839038   O        O     O  O  O  O     O  O     O
228777458   O        O     O        O     O     O  O
83699070   O  O  O  O     O        O     O        O


The O's seem to form letters! They spell out SPR ING SUM MER AUT UMN, or SPRING SUMMER AUTUMN. These are three of the traditional four seasons. The missing one is WINTER, which is therefore the word we need. And another reason this must be right is because of the title: violinist Antonio Vivaldi is known for composing The Four Seasons!

• Very well done, you have all things right! Aug 22 at 4:43