There are four consecutive prime numbers written in

Question

There are four consecutive prime numbers written in ascending order. The product of the first three is 4199 and product of last three is 7429. What is the largest of the four numbers and what is the least of four numbers?

HIMALAYA · Answer

13, 17, 19 and 23.

the cle is 9, the last digits of the product of the primes. we need primes whose unit digits give 9 as unit digit of their products.

Itzrevs · Answer

Prime factorise the numbers 4199 & 7429.

We get the prime numbers 13,17,19,23

So the least of 4 numbers is 13 
and the largest number is 23

TeHCM · Answer

The prime numbers less than 50 are... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41...etc. First three numbers must be around approx 20 ish for the product to be around 4000. 13*17*19 = 4,199 17*19*23 = 7,429 So largest of the four ==> 23 Smallest of the four ==> 13 I used a little intuition and brute force :roll:

laxieqv · Answer

a*b*c = 4199 , b*c*d= 7429 ---> (b*c) * ( d-a) = 3230 = 323*10
Since b*c can't be a multiple of 10 ---> d-a must be a multiple of 10
since 323 has no factors of 2,3,4,5 ,6, 7 (this we can judge by using divisibility tricks) --->  The best d-a is 10  (coz if d-a = 8 or larger ----> there are A LOT other primes in between ----> violate the "consecutive" characteristics of this sequence)

we have 20*20*20= 8000>> 4199 ----> the least number must be < 20
1) a=2 ---> d=12 , not a prime --> out
2) a=3 ---> d= 13, there're 3 primes in between ---> out
3) a=5 --> d=15 , not a prime ---> out
4) a=7 -->d=17 ---> 7,11,13,17 ...but 7*11*13 has unit digit of 1 instead of 9 ---> out
5) a=11 -->d=21 , not a prime --> out
 6) a= 13 ---> d=23 ---> 13,17,19,23 : WOW! 
7) a= 17 ---> d=27, not a prime --> out
8) a= 19 ---> d=29 ---> there's only 1 prime in between ---> out

So the best sequence is 13,17,19,23.

It looks redundant but in fact, the reasoning process is very short and quick.

krisrini · Answer

WOW, easy and nice way to solve this problem. 8-)

Bhai · Answer

Did this an old timer way. Got first 13 and the rest just came.

13, 17, 19, 23

There are four consecutive prime numbers written in

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