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27 Oct 2020, 23:44
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Rule: Any Prime Number greater than >5
must take the Form of:
6k + 1 -or- 6k-1
So we are looking for the Multiples of 6 within the Range of 260 thru 280, and then Add + 1 and Subtract -1
These will be our Test Values
Multiples of 6:
264
270
276
Possible Prime Numbers:
263
265
269
271
275
277
we can Eliminate 265 and 275 because they are Divisible by 5
Remaining Possible Prime Numbers:
263
269
271
277
Since (17)^2 = 289------ we just need to test the Prime Numbers LESS THAN < 17 to see if any Divide Evenly into these 4 Possible Prime Numbers
13 * (20) = 260 ------- 13 * (21) = 260 + 13 = 273
NONE of the 4 Numbers are Divisible by 13
Divisibility by 11:
11 * (24) = 264 --------- 11 * (25) = 275
NONE of the 4 Numbers are Divisible by 13
Divisibility by 7:
7 * (38) = 266 ------- 266 + 7 = 273 ------- 273 + 7 = 280
NONE of the 4 Numbers are Divisible by 7
Since none of the Numbers have Digits that SUM to a Multiple of 3 and of course None are EVEN or End in a Units Digit of 5,
there are 4 Prime Numbers within the Range:
263 ; 269 ; 271 ; 277
must take the Form of:
6k + 1 -or- 6k-1
So we are looking for the Multiples of 6 within the Range of 260 thru 280, and then Add + 1 and Subtract -1
These will be our Test Values
Multiples of 6:
264
270
276
Possible Prime Numbers:
263
265
269
271
275
277
we can Eliminate 265 and 275 because they are Divisible by 5
Remaining Possible Prime Numbers:
263
269
271
277
Since (17)^2 = 289------ we just need to test the Prime Numbers LESS THAN < 17 to see if any Divide Evenly into these 4 Possible Prime Numbers
13 * (20) = 260 ------- 13 * (21) = 260 + 13 = 273
NONE of the 4 Numbers are Divisible by 13
Divisibility by 11:
11 * (24) = 264 --------- 11 * (25) = 275
NONE of the 4 Numbers are Divisible by 13
Divisibility by 7:
7 * (38) = 266 ------- 266 + 7 = 273 ------- 273 + 7 = 280
NONE of the 4 Numbers are Divisible by 7
Since none of the Numbers have Digits that SUM to a Multiple of 3 and of course None are EVEN or End in a Units Digit of 5,
there are 4 Prime Numbers within the Range:
263 ; 269 ; 271 ; 277
29 Jun 2025, 06:07
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
