Odd email
 

I received this email today. The number is not prime, anyone have other ideas?


A senior ranking Non Commissioned Officer here in Iraq has given a group of us a number and no clues to as to what it is. A few of us feel it is something to do with it being a prime number. We are all not math geniuses. So here is where I turn to you for your expert opinion. The number is:

20120121122515626145776622735224615338815731191617

Please assist in any way you can. Thanks for your help.

BTW its factorization is:
20120121122515626145776622735224615338815731191617 = 479 * 133289810174980013 * 315136079611630044400219008571

Just from looking at the number I see it has a quite high number of pairs of digits (...1122...776622 etc.), but in a number of this length, that could be purely coincidental.

Well, looking at it as a substitution cipher, I get the possibilities:

[CODE]20120 tat
1211225 lkve lkby laly lalbe laave
auly auve abkve abkbe abaly abaave abalbe
15 o ae
6 f
26 z bf
14 n ad
5 e
7 g
7 g
6 f
22 v bb
7 g
3 c
5 e
224 vd bx bbd
6 f
15 o ae
3 c
3 c
8 h
8 h
15 o ae
7 g
3 c
119 ki
16 p af
17 q ag[/CODE]

which seems like gibberish in English, though isn't necessarily English even if it is a cipher...

I initially thought it could be a cipher because of the many strings of 2x and 1x in the first half.

Within the number, only
2012012112251562614577662273522461533881
120121122515626145776622735224615338815731191617
6145776622735224615338815731191617
617
17
7
are prime (working from the beginning to end or vice versa, deleting one digit at a time). This is quite a bit lower than most that I've seen (ie from the Homeprime patterns).

I don't know if this is helpful at all, but good luck with it :smile:

[QUOTE=Mini-Geek;144158]BTW its factorization is:
20120121122515626145776622735224615338815731191617 = 479 * 133289810174980013 * 315136079611630044400219008571

Just from looking at the number I see it has a quite high number of pairs of digits (...1122...776622 etc.), but in a number of this length, that could be purely coincidental.[/QUOTE]

back-of-the-envelope calculation:

50 digit number has 49 pairs of digits, the probability that a pair of digits is comprised of the same digit is 10%, so we expect to see about 5 pairs (which includes something like ...12223... counting as 2 pairs).

I count 9 pairs, which is 1.95 standard deviations away (using the binomial distribution), and I think that's right under the 95% confidence interval, so I'd say it's not extraordinary, but I wouldn't be surprised if someone else came along and told me I was wrong

Okay, I give up.

[quote=Prime95;144157]I received this email today. The number is not prime, anyone have other ideas?
20120121122515626145776622735224615338815731191617
[/quote]
I inserted commas as to get numbers between 01 and 26, but in the resulting text I only saw "egg". Upon rot13, I see SMART and other stuff.
[code]
? [20,12,01,21,12,25,15,6,26,14,5,7,7,6,6,22,7,3,5,22,4,6,15,3,3,8,8,15,7,3,11,9,16,17]
? Strchr(Vecsmall(%+vector(#%,i,64)))
"TLAULYOFZN[B]EGG[/B]FFVGCEVDFOCCHHOGCKIPQ"
/*pasted into rot13 */
[SIZE=3]GYNHYLB[/SIZE][B]SMART[/B][SIZE=3]TS[SIZE=3]SIT[/SIZE]PRIQSBPPUUBTPXVCD[/SIZE]
[/code]What's the probability of /accidentally/ getting "SMART", using two elementary/natural encoding methods (# of letter in the alphabet, and rot13) ?

PS: I used the "maximum munch principle" for putting the commas, but maybe military people are less scientific and some other splitting up was intended - I didn't check if something more reasonable can be obtained.
PPS: first I was intrigued by the repetition at the beginning and tried direct ascii conversion using maximum munch principle: 201,201,211,225,156,... but this gives nothing afaics ; b.t.w. it is improbable that the message starts with 2 repeated letters (unless it is to be read from right to left).

The other question is: Do we really want to help officers in Iraq, commissioned or not, help doing their work? I would not, even if I was not too lazy to think about puzzles with no clue whatsoever.

Oops, did I just annihilate my chance of ever getting a visa for the States? H.

[QUOTE=m_f_h;149665]
[/code]What's the probability of /accidentally/ getting "SMART", using two elementary/natural encoding methods (# of letter in the alphabet, and rot13) ?
[/QUOTE]

The chances of getting "SMART"? Infinitesimally small. The chances of getting a 5 letter English word?

29 different five letter sequences (incorrectly assuming independence), roughly 8600 5 letter words in the English language, the chances of NONE of the sequences containing a word is (1-8600/26^5)^29

...so about 1 out of 50.

(if you don't like my independence assumption, we can take the 7 different blocks of letters that don't interact for a lower bound. That gives us about 1 out of 200)

A possible clue:

[spoiler]
The first 11 digits are all 0, 1 or 2.
[/spoiler]

Digit counts:

0 appears 2 times
1 appears 12 times
2 appears 10 times
3 appears 4 times
4 appears 2 times
5 appears 6 times
6 appears 6 times
7 appears 5 times
8 appears 2 times
9 appears 1 time

There is a rather uneven distribution of digits, and most digits appear an even number of times. Of course all of this could be chance...

A) Since there are 50 digits, I spread them out in rows of 5:

[code]
A) B) C)
2 0 1 2 0 VA 2 0 1 2 0
1 2 1 1 2 NY 1 - - - -
2 5 1 5 6 WV 2 - - - -
2 6 1 4 5 WV 2 - - - -
7 7 6 6 2 TX 7 - - - -

2 7 3 5 2 NC 2 - - - -
2 4 6 1 5 VA 2 - - - -
3 3 8 8 1 FL 3 - - - -
5 7 3 1 1 SD 5 7 3 1 1
9 1 6 1 7 CA 9 1 6 1 7
[/code]B) Since five of the ten groups started with '2', I began to think of zip codes. (All the zip codes around Wash DC start with 2, so this stood out). So, I put the state letters beside each group of 5.

C) I fed them into a zip code lookup function, forwards, backwords, down, and up, but only found 5 valid codes (out of 40):

Forwards:
20120 ... ... Sully Station:Fairfax:VA
57311 ... ... Farmer:Hanson:SD
91617 ... ... Valley Village:Los Angeles:CA

Backwords: nothing

Down:
21227 ... ... Baltimore:Baltimore:MD

Up:
95322 ... ... Santa Nella:Merced:CA

Diagonals: nothing

I found it really peculiar that the only digits that made valid zip codes were along the top, left, and bottom of my chart. I'm sure it's just coincidence though.

I don't have any more zip code ideas. I'm posting here to possibly spur someone else on :smile:

It's kind of odd that the number starts with a 2, then two entries of 012.

I wonder if somebody left out some character code indicator, e.g.:
2 0x12 0x12 1122515626145776622735224615338815731191617

Now, 12 could be a form feed character; or it could be the size of something.

Removed speculation that didn't add up...

OK, I give up for now.