Question

How many possible pairs of prime numbers are there if the difference between the two prime numbers is 2 and both numbers are less than 50? list all the pairs.

Answer 1

so a prime is odd except for 2
let's assume the prime number is greater than 2 since there is no prime number such that the different of the prime number and 2 is 2
ok we have some odd number in the form of n=2k+1
and another prime m=2j+1
assume 50>m>n>0 (assuming we are talking about positive primes)
so m-n=2
m=2+n
m=2+(2k+1)
m=2k+3
2j+1=2k+3
2j=2k+2
j=k+1

so we know j=k+1

so we can write our prime numbers as
n=2k+1
m=2(k+1)+1=2k+2+1=2k+3

all the pairs will be of this form:
(2k+3,2k+1)

Answer 2

and i suppose we should assume k>0 since if k=0 we get 1 is in our set
and 1 is not prime

Answer 3

some of examples:
so if k=1: (5,3)
if k=2: (7,5)
k=3: 3 will not work (we get a number that is not prime)
k=4: 4 will not work
k=5: 5 will not work
k=6: 6 will not work
k=7: 7 will not work
k=8: (19,17)
k=9: 9 will not work
k=10: 10 will not work

Answer 4

14 is the next one that works (31,29)

Answer 5

then 20: (43,41)

Answer 6

25: (53,51)

Answer 7

28: (59,57)
29: (61,59)
35: (73,71)
43: (89,87)
44: (91,89)
50: (103,101)

Answer 8

i think all these pairs are composed of primes

Answer 9

You must have missed the part where it said the numbers had to be less than 50

Answer 10

oops i did for k=50
lol

Answer 11

yes you are right i forgot basically

Answer 12

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Answer 13

lol

Answer 14

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Answer 15

you have been waiting for me to fail i see :(

Answer 16

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Answer 17

You're my favorite computer

Answer 18

:)

Answer 19

How come you're always on here all the time? You could be working as a private tutor and making a lot of money....

Answer 20

thanks for making the process quicker hero

Answer 21

i don't like in person

Answer 22

i like to choose if i want to help someone

Answer 23

You can choose your own hours, etc...

Answer 24

i don't wanna

Answer 25

lol

Answer 26

I'm not kidding