night yogi summer moons
Good morning everyone it's a little cloudy this morning, I hope we get some rain but it's not looking likely.
Enjoy your day everyone 
Good morning everyone
Cloudy here at present but forecast to remain dry.
Yogi, well done on that cricket quiz - you must know more than you thought to get a perfect 10 out of 10 
The base covering of the pavement past my house should be done this morning so there's a risk that my Viegin Media cable could get hit by the heavy roller.
I hope everyone has a good day
Gargoyles on cathedrals and older churches have been around for centuries. They are stone carvings on the outside near to top and are used to channel rain water from the roof away from the walls through their mouths. 6 more gargoyles are to be installed at Gloucester cathedral representing various districts of Gloucestershire.
https://www.bbc.co.uk/news/uk-...cestershire-48459590
The ones mentioned are of a suffragette (Annie Kenney for Stroud), a rugby player for Gloucester, a horse jockey for Cheltenham) and the strangest one a cheese roller which they say represents Tewkesbury. Coopers Hill of cheese rolling fame is south east of Gloucester, south of Cheltenham. Tewkesbury is north of Gloucester and Cheltenham so a bit odd.
Good morning everyone.
Still raining up here 
El, I think my score was down to luck - although some of the correct phrases were familiar to me, which is why I chose them as my answer.
Iâm glad the Annie Kenny gargoyle will not be grotesque 
Fingers crossed that heavy roller doesnât damage your Virgin cable
Summer, I hope you enjoyed your cake
Have a good day, all.
El Loro posted:Yogi, you must be very lucky as to get 8 guesses correct is a 1 in 256 chance
Iâm not usually lucky, El. Perhaps I picked up more than I realised when hubby was watching once day cricket matches.
Just in case my luck holds out, I might buy a Euromillions ticket for tonight.
Yogi19 posted:El Loro posted:Yogi, you must be very lucky as to get 8 guesses correct is a 1 in 256 chance
Iâm not usually lucky, El.
Just in case my luck holds out, I might buy a Euromillions ticket for tonight.
There was an item on yesterday's Today programme on Radio 4 called "If Britain was a piece of music, what would it be?" about a new book linking music with British landscape. The article covered different genres of music but started and ended with one peace. No prizes for guessing which one 
https://www.youtube.com/watch?v=wbFi85piaEg
Yes, you were correct
Listening to the Infinite Monkey Cage on Radio 4 and they had this poser.
You are asked a question, you think of an answer, then you you think that may be wrong and a second answer comes to mind.
The poser is which answer is more likely to be correct, your initial thought or your second thought? This poser only relates to where you do have a second thought.
It seems that the second thought is more likely to be correct than the first thought,
And now a puzzle for you.
What number is next in the sequence of numbers?
11
101
191
If you answer 281 that would be correct. That's the more straightfoward answer - just add 90 each time.
However if you answered 821 that would also be correct. However that is considerably harder. It's to do with prime numbers. For anyone who hasn't stopped reading they are what are called prime quadruplets. That's because 11,13,17 and 19 are prime numbers, as are 101,103,107 and 109 ; 191,193,197 and 199; and 821,823,827 and 829. As numbers which end in 5 are divisble by 5 it's impossible for 15,105,195 or 825 to be prime numbers so those have to be ignored.
By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876
El Loro posted:There was an item on yesterday's Today programme on Radio 4 called "If Britain was a piece of music, what would it be?" about a new book linking music with British landscape. The article covered different genres of music but started and ended with one peace. No prizes for guessing which one
https://www.youtube.com/watch?v=wbFi85piaEg
Yes, you were correct
Good choice
El Loro posted:And now a puzzle for you.
What number is next in the sequence of numbers?
11
101
191
If you answer 281 that would be correct. That's the more straightfoward answer - just add 90 each time.
However if you answered 821 that would also be correct. However that is considerably harder. It's to do with prime numbers. For anyone who hasn't stopped reading
I got 281
prime quadruplets are beyond me
El Loro posted:By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876
Did you say that explained it in simple terms?!
Yogi19 posted:El Loro posted:By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876Did you say that explained it in simple terms?!
I did say relatively simple terms
Here's a more complex article:
https ://en.wikipedia.org/wiki/RSA_(cryptosystem) (this forum doesn't work for some Wiki articles because of the syntax used - you would need to copy that address into your browser bar and remove the space I've put after https to be able to get to the article).
Here's just one sentence from it:
"Compute Îŧ(n), where Îŧ is Carmichael's totient function. Since n = pq, Îŧ(n) = lcm(Îŧ(p),Îŧ(q)), and since p and q are prime, Îŧ(p) = Ï(p) = p â 1 and likewise Îŧ(q) = q â 1. Hence Îŧ(n) = lcm(p â 1, q â 1)"
El Loro posted:Yogi19 posted:El Loro posted:By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876Did you say that explained it in simple terms?!
I did say relatively simple terms
Here's a more complex article:
https ://en.wikipedia.org/wiki/RSA_(cryptosystem) (this forum doesn't work for some Wiki articles because of the syntax used - you would need to copy that address into your browser bar and remove the space I've put after https to be able to get to the article).
Here's just one sentence from it:
"Compute Îŧ(n), where Îŧ is Carmichael's totient function. Since n = pq, Îŧ(n) = lcm(Îŧ(p),Îŧ(q)), and since p and q are prime, Îŧ(p) = Ï(p) = p â 1 and likewise Îŧ(q) = q â 1. Hence Îŧ(n) = lcm(p â 1, q â 1)"
Consider me well and truly baffled
Goodnight and sweet dreams, El and Ros
Hug for any night owls
Good evening a dark & dreary day here, with around 5 mins of brilliant sunshine as I ate my tea! A pleasant day all round though, I hope youâve all had a good Friday
Yogi19 posted:Goodnight and sweet dreams, El and Ros
Hug for any night owls
Sweet dreams yogi
Sweet dreams everyone I hope you have a joyful weekend
El Loro posted:Gargoyles on cathedrals and older churches have been around for centuries. They are stone carvings on the outside near to top and are used to channel rain water from the roof away from the walls through their mouths. 6 more gargoyles are to be installed at Gloucester cathedral representing various districts of Gloucestershire.
https://www.bbc.co.uk/news/uk-...cestershire-48459590
The ones mentioned are of a suffragette (Annie Kenney for Stroud), a rugby player for Gloucester, a horse jockey for Cheltenham) and the strangest one a cheese roller which they say represents Tewkesbury. Coopers Hill of cheese rolling fame is south east of Gloucester, south of Cheltenham. Tewkesbury is north of Gloucester and Cheltenham so a bit odd.
love cathedrals and Gargoyles EL but in a more traditional way
Yogi19 posted:El Loro posted:By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876Did you say that explained it in simple terms?!
agree yogi
Yogi19 posted:El Loro posted:Yogi19 posted:El Loro posted:By the way, if you want to know how prime numbers have their uses, one major way is encryption. This article attempts to explain it in relatively simple terms:
https://www.abc.net.au/news/sc...yption-works/9338876Did you say that explained it in simple terms?!
I did say relatively simple terms
Here's a more complex article:
https ://en.wikipedia.org/wiki/RSA_(cryptosystem) (this forum doesn't work for some Wiki articles because of the syntax used - you would need to copy that address into your browser bar and remove the space I've put after https to be able to get to the article).
Here's just one sentence from it:
"Compute Îŧ(n), where Îŧ is Carmichael's totient function. Since n = pq, Îŧ(n) = lcm(Îŧ(p),Îŧ(q)), and since p and q are prime, Îŧ(p) = Ï(p) = p â 1 and likewise Îŧ(q) = q â 1. Hence Îŧ(n) = lcm(p â 1, q â 1)"
same here
equate prime numbers to binary numbers (0,1) - computer language don't know why
night yogi moons summer
Good morning everyone. My goodness what a warm night! That came from nowhere. I don't know whether it was just down here in Devon but if it was warm where you are I hope you slept well.
Enjoy your day everyone
Good morning everyone
Sunny and a warm day here. Squiggle, I thnk the weather for the southerm half of the country is expected to be hot in places particularly in the east - I think it's just for today though.
Ros, like you I find the idea of modern gargoyles a bit odd 
I hope everyone has a good day
Ros, on the subject of prime numbers and binary numbers there's no direct connection for all primes as such though binary numbers have been used by computers when trying to see if a number is prime or not.
As I mentioned, that's for primes generally but there is a subset where there is a direct connection with binary numbers and that's Mersenne primes. A Mersenne prime number is a prime number of the format 2 to the power of a number (n) less 1. For instance for n = 3, 2 to the power of 3 = 8 less 1 = 7 which is a prime number. If n = 7 , the result is 127 which is also prime. If you understand binary numbers you will realise that all Mersenne primes consist of 1s in binary, 127 in binary is 1111111 for instance.
Mersenne numbers are directly connected with perfect numbers. Such a perfect number is of the format 2n-1(2n - 1), If n is 7 the result is 8128. If you were to list all the numbers which are its proper divisors (including 1) and add then up you'd get 8128. Such a perfect number in binary will always start with a series of 1s and then a series of 0s. 8128 in binary is 1111111000000.
Ros, as an addendum to the above, n is always a prime number itself but not all prime numbers used for n result in a Mersenne prime - very few do.
Also, as far as I know it's still unproven that there are no odd perfect numbers (using a different format to Mersenne primes) though none has been found,
Good morning a sunny start here, I even had my breakfast outside and grabbed the opportunity to spray weed killer on the patio
squiggle, itâs definitely not hot here, I woke up quite chilly and to find bramble curled up against my shoulder! Iâll happily swap your heat for the rain weâve been having
At present the highest known prime number, a Mersenne prime, is 282,589,933 â 1. So in binary that's 82,589,933 1s.
It's not known if there's a finite number of Mersenne primes. There is an infinite number of prime numbers. That's easy to prove - if you were to multiple every prime number known (ignoring 2) together and deduct 1 or 2 (doesn't matter which) you would get a number which cannot be divided by any of those numbers so it has to be either a prime number or a multiple of prime numbers not known.
As mentioned above a perfect number is one where the sum of its proper divisors is itself. For instance the proper divisors of 28 are 1,2,4,7 and 14 and the sum of those is 28.
There are also amicable numbers, that's 2 numbers where the sum of the propert divisors of one number is the other and vice versa. The lowest amicable numbers are 220 and 284.
Proper divisors of 220 are 1,2,4,5,10,11,20,22,44,55 and 110 which total 284,
Proper divisors of 284 are 1,2,4,71 and 142 which total 220.
Perfect numbers and amicable numbers are types of sociable numbers where the sum of the proper divisors of a number leads to a number where the sum of the proper divisors leads to a number and cycles on until you get back to the original number. In the case of perfecr numbers, the length of the cycle is just the 1 number and for amicable numbers just the 2 numbers. There are longer cycles, the longest one known consists of 28 numbers and starts with 14316.
There are also friendly numbers which are different to the above though,
The pupil who interprets for teachers for other pupils:
https://www.bbc.co.uk/news/vid.../headlines/48404081/
Evening all
Weather was cloudy this morning, then brightened up in the afternoon.
El, I like the idea of friendly numbers
I hope youâve all had a good day
Goodnight and sweet dreams, Ros
Hug for the night owls
El Loro posted:Good morning everyone
Sunny and a warm day here. Squiggle, I thnk the weather for the southerm half of the country is expected to be hot in places particularly in the east - I think it's just for today though.
Ros, like you I find the idea of modern gargoyles a bit odd
I hope everyone has a good day
didn't like the modern gargoyles TBH EL
El Loro posted:Ros, as an addendum to the above, n is always a prime number itself but not all prime numbers used for n result in a Mersenne prime - very few do.
Also, as far as I know it's still unproven that there are no odd perfect numbers (using a different format to Mersenne primes) though none has been found,
love these posts EL - you obviously have a very astute mathematical brain well above me
El Loro posted:The pupil who interprets for teachers for other pupils:
https://www.bbc.co.uk/news/vid.../headlines/48404081/
had personal experience of this - awesome