prime spam

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fruitmonster97

2481 posts

fruitmonster97

#1 h Nov 7, 2024, 4:54 PM

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What is the sum of the digits of the smallest prime that can be written as a sum of $5$ distinct primes?

$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }11$

This post has been edited 1 time. Last edited by fruitmonster97, Nov 7, 2024, 8:21 PM

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fruitmonster97

2481 posts

fruitmonster97

#2 h Nov 7, 2024, 4:56 PM

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If $2$ was one of the primes, then the sum would be even, impossible. Otherwise, $3+5+7+11+13=39,$ which isn't prime, but $3+5+7+11+17=43\implies{7}$ is, yielding $\boxed{\textbf{(B)}}.$

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MathRook7817

662 posts

MathRook7817

#3 h Nov 7, 2024, 4:58 PM • 1 Y

Y by mithu542

The minimum possible sum of 5 distinct primes that are odd (since the number is prime) is
3+5+7+11+13 = 39
41 is impossible since 15 isn't prime, so the number is 43 (3+5+7+11+17).
Therefore, the answer is 4+3 = 7 (B)

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Jonysun

34 posts

Jonysun

#4 h Nov 7, 2024, 4:59 PM

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The answer is indeed $\fbox{43} \Rightarrow B$

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golden_star_123

206 posts

golden_star_123

#5 h Nov 7, 2024, 5:16 PM

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All the primes have to be odd for the sum to be odd. We may then just bash out the possibilities to notice that the first prime that works is $43$ , so the answer is $\boxed{7}$ .

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gracemoon124

872 posts

gracemoon124

#6 h Nov 7, 2024, 5:35 PM • 2 Y

Y by alexanderhamilton124, songyanxin

sillied ):

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lpieleanu

2918 posts

lpieleanu

#7 h Nov 7, 2024, 5:38 PM

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Solution

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SomeonecoolLovesMaths

3203 posts

SomeonecoolLovesMaths

#8 h Nov 7, 2024, 6:06 PM

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$3+5+7+11+17=43$ 7 confirmed

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wangzrpi

159 posts

wangzrpi

#9 h Nov 7, 2024, 6:10 PM

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4+3=7 confirmed

Cannot be 2 because then the sum would be even and therefore not prime

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KenWuMath

58 posts

KenWuMath

#10 h Nov 7, 2024, 6:16 PM

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apparently 15 isnt a prime

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wangzrpi

159 posts

wangzrpi

#11 h Nov 7, 2024, 6:51 PM

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fruitmonster97 wrote:

If $2$ was one of the primes, then the sum would be even, impossible. Otherwise, $3+5+7+11+13=39,$ which isn't prime, but $3+5+7+11+17=43\implies{7}$ is, yielding $\boxed{\textbf{(B)}}.$

Also sum of primes 5-13 is larger

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dolphinday

1325 posts

dolphinday

#12 h Nov 7, 2024, 7:19 PM

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I did 11 + 13 = 14 on this one. double checked it too

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GreenBanana666

548 posts

GreenBanana666

#13 h Nov 7, 2024, 7:21 PM

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Its $43$ , $4+3=7$ . Its B then

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SkatingKitty

223 posts

SkatingKitty

#14 h Nov 7, 2024, 7:51 PM

Y by

I miscalculated and and got 53, or 8 chat I’m cooked again

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mhgelgi

668 posts

mhgelgi

#15 h Nov 7, 2024, 7:53 PM • 1 Y

Y by SkatingKitty

SkatingKitty wrote:

I miscalculated and and got 53, or 8 chat I’m cooked again

yeah, same here, we can weep together

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SkatingKitty

223 posts

SkatingKitty

#16 h Nov 7, 2024, 8:00 PM

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I literally left like all of them blank except for like 2 that I got wrong

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mhgelgi

668 posts

mhgelgi

#17 h Nov 7, 2024, 8:01 PM

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127.5 => 103.5 (4 sillies)

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SkatingKitty

223 posts

SkatingKitty

#18 h Nov 7, 2024, 8:08 PM

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2 sillies- probably bc I don’t know abt my other ones lol

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happypi31415

742 posts

happypi31415

#19 h Nov 7, 2024, 8:12 PM

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I put 53 like an idiot

This post has been edited 2 times. Last edited by happypi31415, Nov 8, 2024, 5:25 PM

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SkatingKitty

223 posts

SkatingKitty

#20 h Nov 7, 2024, 8:14 PM

Y by

Not the only one here

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SirAppel

877 posts

SirAppel

#21 h Nov 7, 2024, 8:15 PM

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answer choice E was 11, and I know that because I almost put E before checking my answers oops (47 susus)

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SkatingKitty

223 posts

SkatingKitty

#22 h Nov 7, 2024, 8:19 PM

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At least you caught your mistake: I forgot to check my answers

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gicyuraok2

1059 posts

gicyuraok2

#23 h Nov 7, 2024, 11:26 PM

Y by

i for sure would have had to come back to this lol

obv i looked at $5+7+11+13+17=53$ first, but $8$ isn't one of the answers (thank god)
accidentally got a spoiler but probably would have found it anyway

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Existing_Human1

209 posts

Existing_Human1

#24 h Nov 7, 2024, 11:42 PM

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POV: Your nervousness causes you to think that 2 + 3 + 5 + 7 + 11 is odd

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SkatingKitty

223 posts

SkatingKitty

#25 h Nov 8, 2024, 1:29 AM

Y by

gicyuraok2 wrote:

i for sure would have had to come back to this lol

obv i looked at $5+7+11+13+17=53$ first, but $8$ isn't one of the answers (thank god)
accidentally got a spoiler but probably would have found it anyway

Rly? Oh whoops I put 8

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mathenrichmentaops

539 posts

mathenrichmentaops

#26 h Nov 8, 2024, 2:54 AM

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SkatingKitty wrote:

gicyuraok2 wrote:

i for sure would have had to come back to this lol

obv i looked at $5+7+11+13+17=53$ first, but $8$ isn't one of the answers (thank god)
accidentally got a spoiler but probably would have found it anyway

Rly? Oh whoops I put 8

Omg same I think I changed it to B tho

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gicyuraok2

1059 posts

gicyuraok2

#27 h Nov 9, 2024, 8:48 PM

Y by

mathenrichmentaops wrote:

SkatingKitty wrote:

gicyuraok2 wrote:

i for sure would have had to come back to this lol

obv i looked at $5+7+11+13+17=53$ first, but $8$ isn't one of the answers (thank god)
accidentally got a spoiler but probably would have found it anyway

Rly? Oh whoops I put 8

Omg same I think I changed it to B tho

how do you put 8 if it's not one of the answer choices

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