# Onion 7: numbers on page 15

*139*pages on

this wiki

This article discusses the code that appears on **page 15** of the document received from Onion 7. The code itself features a 4x4 table of numbers. A number of approaches and tests have been applied to this code to determine the meaning, as it is one of the few things in the 58-page codebook that is not written in runes.

## The numbersEdit

The table of numbers as they appear in the image from Onion 7:

3258 3222 3152 3038 3278 3299 3298 2838 3288 3294 3296 2472 4516 1206 708 1820

It should be noted that all of the numbers are even except 3299, and that 3299 itself is prime.

## Sums of the numbersEdit

Summing the rows and columns were one of the first tests against the numbers:

3258 + 3222 + 3152 + 3038 = 12670 + + + + + 3278 + 3299 + 3298 + 2838 = 12713* + + + + + 3288 + 3294 + 3296 + 2472 = 12350 + + + + + 4516 + 1206 + 708 + 1820 = 8250 = = = = = 14340+ 11021+ 10454+ 10168 = 45983

Of particular note, the sums of second row and second column are the only ones to feature odd numbers: 12713 and 11021. *However, only 12713 is prime.

Diagonal sums were performed on the table as well (shown below, with unused numbers removed):

=14146 3258 3038 + + 3299 3298 + 3294 3296 + + 4516 1820 =11673

Neither of the results here were prime.

## Table of primesEdit

It was realized by one user investigating the page that subtracting (or adding) each of the numbers from 3301 would yield a table of **prime numbers**! (eg. 3301-3258=43). This table is shown below:

43 79 149 263 23 2 3 463 13 7 5 829 7817 4507 2593 1481

### InconsistenciesEdit

Of particular interest, all of the values except the last two follow the form 3301-X where the last two follow the form 3301+X.

One possible reason for this is because the next values in the table could not be represented with 4 digits using the original formula. On the other hand, other users have felt this may be some sort of signal.

In some cases, this fact has lead to doubt over the pattern, however using given values to result in primes fitting a predetermined pattern with a single operation is an extremely low-probability event.

### Conversion to order valuesEdit

All prime numbers appear in the sequence P={2,3,5,7, ...}. In this sequence, a particular prime number can be represented as Pn (for example P3) where 'n' is the "order" (position in the sequence).

If we consider 2 to be of order 0 (P0), then 3 is of order 1, and so on - such that P0,P1,P2,P3 represent the prime numbers 2,3,5,7. Using this relationship we can represent the table by their position in the sequence of all prime numbers. Here is the table of their positions:

13 21 34 55 8 0 1 89 5 3 2 144 987 610 377 233

### SpiralsEdit

Infographic: http://i.imgur.com/dS9wLm1.png

Considering either the Table of Primes, or the Order Table:

If you read the numbers starting at the lowest value and continuing in ascending value, the path you take along the table will form a spiral. This spiral can be created using a recursive function (like the Fibonacci sequence), where the next value is the sum of a couple previous values.

For example: ......13, 21, 34(13+21), 55(21+34), 89(34+55)......etc

In the Order Table, *all of the values in the spiral are Fibonacci numbers* starting at Fib(0), and the spiral could be extended further (to infinity). This function cannot be applied to the Table of Primes, and the likelyhood of a function producing primes is low - however, using a list of primes, this spiral can be extended as well.

One hypothesis is that the person who generated the numbers used the Fibonacci sequence to select numbers from a list of primes, then added 3301 as a level of obscurity. It is still unknown what information we are supposed to gain from this puzzle.

Note: Because the original table of numbers deceases in value on the last line, this pattern does not hold for it specifically, but will fit the Table of primes or Order Table perfectly. Some have speculated that this detail might imply that the sequence oscillates to return to begin again in a mobius type loop.

### Related snippetsEdit

Note: this section has not been verified or cleaned up.

fibonacci sequence! F(7) F(8) F(9) F(10) F(6) F(0) F(1/2) F(11) F(5) F(4) F(3) F(12) F(16) F(15) F(14) F(13) F(17) F(26) F(25) F(24) F(18) F(27) F(28) F(23) F(19) F(20) F(21) F(22) Not j28 addition ust fibonacci sequence but it also begins a mobius loop... 0-14 e subtraction, 15- a thing that look like an 8, a loop, a mobius strip, or an infinity sign 3299 is the only prime in there

## **Another Explanation** Edit

This number square is related to Zeckendorf's Theorem: if we count in ascending powers in the Fibonacci-base number system you can exactly reproduce the spiral:

http://cicada3301.boards.net/thread/35/fibonacci-prime-spiral-zeckendorfs-theorem

## 2 more links with explanation how spiral matrix was formed Edit

https://docs.google.com/spreadsheets/d/1ammrDDnnLC5kndOJCsxwcMNNyu4N2Puy9w1p241fSSo/edit#gid=0

https://www.reddit.com/r/codes/comments/4oz0fv/solve_this_text_in_furthark_language/