prime number challenge

[Don Shepherd]

I see in the newspaper today that Amazon Prime Air's first aircraft has a tail number that contains a "prime" number, 1997. I wonder how Amazon staff verified that 1997 is prime. Perhaps they called some geek on this forum!

After I retired a few years ago, I needed a part-time job while I was attending university to get my teaching degree so I could become a math teacher. I signed up with Beeline Courier Service, which was a barrel of fun driving around the city picking up and delivering things. Every courier had a 4-digit courier number that was used to identify him/her on the two-way radio. My assigned 4-digit courier number ending in 41 was a prime number. I eventually resigned from the courier job but returned a couple of years later and my new courier number was exactly 700 more than my first courier number, again ending in 41, and it was a prime number also.

My first courier number was the first 4-digit number (first digit can't be 0) ending in 41 that is prime. What was my first courier number and my second courier number?

Prize for the person with the first correct answer: an "attaboy."

[Gerson W. Barbosa]

The sum of digits of their product is 35.

[Don Shepherd]

Congratulations Gerson, you get the "attaboy".

[Gerson W. Barbosa]

I got married on xx/xx/xxxx (the date looks the same either in European or in American format), date elements being prime numbers. The sum of the eight digits in the date is exactly 2016 minus xxxx again a prime number. Just prime coincidences, not enough information to make for another prime challenge, I think. So no attaboy, no yo-da-man.

[Paul Dale]

(08-07-2016 05:24 AM)Gerson W. Barbosa Wrote:  I got married on xx/xx/xxxx (the date looks the same either in European or in American format), date elements being prime numbers. The sum of the eight digits in the date is exactly 2016 minus xxxx again a prime number. Just prime coincidences, not enough information to make for another prime challenge, I think. So no attaboy, no yo-da-man.

More than enough information to make for a challenge. Just not a really difficult one. Still I love the coincidences present.

2/2/87 perchance?


- Pauli

[Gerson W. Barbosa]

(08-07-2016 05:53 AM)Paul Dale Wrote:  More than enough information to make for a challenge. Just not a really difficult one. Still I love the coincidences present.

2/2/87 perchance?

No, not enough information had been provided, but you got close. Yet another coincidence: the sum of digits of this year's wedding anniversary date will be a prime number too (however this still wouldn't have granted a unique solution, unless I had said the anniversary hadn't occurred yet). Now I have to take care not to forget about the date like I did last year. Why do wives get so upset when we do? :-)

Gerson.

[Paul Dale]

(08-07-2016 11:56 AM)Gerson W. Barbosa Wrote:  No, not enough information had been provided, but you got close. Yet another coincidence: the sum of digits of this year's wedding anniversary date will be a prime number too (however this still wouldn't have granted a unique solution, unless I had said the anniversary hadn't occurred yet).

Ah, I know now A mistake in my earlier analysis I'm afraid.

Quote:Now I have to take care not to forget about the date like I did last year. Why do wives get so upset when we do? :-)

We cannot know the unknowable....

However, it wouldn't be difficult to remember in some countries


Pauli

[Gerson W. Barbosa]

(08-07-2016 12:22 PM)Paul Dale Wrote:  Ah, I know now A mistake in my earlier analysis I'm afraid.

You're da man! No, not a mistake, just insufficient information as 0 + 2 = 1 + 1. My fault, actually.

Speaking of prime-related coincidences, in early 1979 I went to Law School for a couple of weeks before quitting. My candidate number to the admittance exam was 109. In July that year I joined the military. My student number in the Air Force technical school was 79-1097. Three years later when I began a Physics course at the university my student number was 82-0971-5. Except for 82, all numbers here are primes, mostly involving the digits 0, 1, 7 and 9. But there's more: my second bank account number in 1981, six or seven digits long, involved only those four digits, like my number at the Air Force (not related to my initial student number) and my number as an EE student some years later.

Gerson.

[Massimo Gnerucci]

(08-07-2016 04:29 PM)Gerson W. Barbosa Wrote:  

(08-07-2016 12:22 PM)Paul Dale Wrote:  Ah, I know now :) A mistake in my earlier analysis I'm afraid.

You're da man! No, not a mistake, just insufficient information as 0 + 2 = 1 + 1. My fault, actually.

Speaking of prime-related coincidences, in early 1979 I went to Law School for a couple of weeks before quitting. My candidate number to the admittance exam was 109. In July that year I joined the military. My student number in the Air Force technical school was 79-1097. Three years later when I began a Physics course at the university my student number was 82-0971-5. Except for 82, all numbers here are primes, mostly involving the digits 0, 1, 7 and 9. But there's more: my second bank account number in 1981, six or seven digits long, involved only those four digits, like my number at the Air Force (not related to my initial student number) and my number as an EE student some years later.

Gerson.

Well, all these coincidences surely are not against all odds... :P

[Paul Dale]

(08-07-2016 05:40 PM)Massimo Gnerucci Wrote:  Well, all these coincidences surely are not against all odds...

Or cherry picked numbers -- the question to ask is how many other numbers weren't prime?

Lots I'd guess. The first bank account number is stated. What about car number plates? Driver's licence number? Passport number?


Pauli

[Gerson W. Barbosa]

About 12% of all 4-digits number are primes, but what has stricken me are the ones involving the digits 0, 1, 7 and 9. But then again we are given so many numbers that coincidences like these are likely to occasionally occur.

[TASP]

has any individual demonstrated a talent for IDing primes by sight ??

[Claudio L.]

(08-08-2016 04:15 PM)TASP Wrote:  has any individual demonstrated a talent for IDing primes by sight ??

Chances of correctly identifying a relatively small prime (let's say 4 digits) are not too bad:
* The number has to end in 1,3,7 or 9 (disregarding the obvious 2 and 5), this alone allows you to discard 60% of the numbers.
* Quick divisibility by 3 by sum of digits: this one discards other 13% roughly.

So you can easily discard 73% of the numbers, then out of the 2700 numbers that passed the 2 tests above, 1227 are primes (total primes = 1229, less the numbers 2 and 5). So you have roughly a 45% chance of detecting a prime number <10000 at naked eye.
Almost a coin flip.

Now if you want more accuracy, *just* memorize all these:

Divisibility rules up to 50

[TASP]

I was thinking more of the folks that can look at a photo of pebbles or some such, and more or less instantly give an accurate total of how many there are.

So would it even be possible theoretically for a person to look at a 10 digit number and ascertain in a few seconds whether or not it's prime ??

[EdS2]

(08-08-2016 06:29 PM)TASP Wrote:  I was thinking more of the folks that can look at a photo of pebbles or some such, and more or less instantly give an accurate total of how many there are.

So would it even be possible theoretically for a person to look at a 10 digit number and ascertain in a few seconds whether or not it's prime ??

Oliver Sacks famously met a pair of twins in 1966 who seemed to have such powers. But probably they didn't. There's a writeup and video at
http://www.pepijnvanerp.nl/articles/oliv...e-numbers/