#Which is the only natural number from 1 to 30 that cannot be expressed either as the sum of any two
grand wedge
fluid mulchBOT
dawn obsidian
tender zenith
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
2 = 7-5
3 = 5-2
4 = 17-13
5 = 2+3
6 = 11-5
7 = 2+5
8 = 3+5
9 = 11-2
10 = 23-13
11 = 13-2
12 = 5+7
13 = 2+11
14 = 17-3
15 = 2+13
16 = 19-3
17 = 19-2
18 = 23-5
19 =2+17
20 = 23-3
21 = 23-2
22 = 29-7
23
24 = 11+13
25 = 2+23
26 = 29-3
27 = 29-2
28 = 11+17
29 = 31-2
30 = 13+17
23 can't be written like that. But neither can 29, unless you use 31 and 2, and 31 is not in the range 2 to 30.
Thing is, how can you be sure there aren't any prime numbers out of the range 2 to 30 such that their difference is 23? Cause you see, you can go as far as 991 and 997, and those are still prime numbers, and their difference is 6. So I don't see a way you can make sure there aren't any prime numbers "x" and "y" such that "x-y = 23". So, is it really true that 23 can't be written as the difference of any two prime numbers? Not in the range 2 to 30, no. But then, 29 can't be written as the sum or the difference of prime numbers in that range either. You need 31 minus 2.
Here is a list of all prime numbers below 1000:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
Edited following un_decorateur's suggestion.
grand wedge
is there a proper expression or equation that shows this
and i aso heard about 2 number theories ... Goldbach Conjecture and the corollary ....
are they true?
tender zenith
I don't think there is any expression you can use to get all prime numbers. There is an ancient method called "Sieve of Eratosthenes". It's a very lengthy process.
grand wedge
is it relevant for O level maths D?
grand wedge
is it relevant for O level maths D?
.,...
sweet mist
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
2 = 7-5
3 = 5-2
4 = 17-13
5 = 2+3
6 = 11-5
7...
two different primes
4 = 17 - 13
6 = 11 - 5
10 = 7 + 3
14 = 17 - 3
22 = 29 - 7
26 = 23 + 3
sweet mist
and i aso heard about 2 number theories ... Goldbach Conjecture and the corollar...
the Goldbach conjecture hasn't yet been proven
the odd Goldbach Conjecture (a corollary) seems to be proven by Harald Helfgott
which says that an odd number can be the sum of 3 prime numbers
grand wedge
23 is an exception to these 2 theories
sweet mist
23 is an exception to these 2 theories
23 is an odd number so the Goldbach conjecture doesn't care (Goldbach Conjecture is about even number)
and the odd Gold. conjecture gives a decomposition with 3 primes, that not interset us
sweet mist
so 23 is basically an exception
it is more accurate to say that the odd Goldbach Conjecture is not related to our problem because the odd Gold. conjec. gives a decomposition with 3 primes
and we want a decomp. with only 2 primes
sweet mist
how would you explain that?
I found the reason why 23 cannot be decomp as 23 = p + q or 23 = p - q
because
Even ± Even = Even
Even ± Odd = Odd
Odd ± Even = Odd
Odd ± Odd = Even
So p is even and q odd or the opposote p is odd and q even
But there is only one even prime, this is 2.
So one of the orime must be 2.
23 = p+2 or 23=p-2
but in the first case p = 21 not prime
and in the second case p= 25 not prime
grand wedge
I found the reason why 23 cannot be decomp as 23 = p + q or 23 = p - q
becaus...
this must hellp thanku
is this relevant for my O lvel maths D course?, it was in the book btw
sweet mist
this must hellp thanku
!done
fluid mulchBOT
this must hellp thanku
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sweet mist
is this relevant for my O lvel maths D course?, it was in the book btw
idk I'm french
grand wedge
party
sweet mist
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sweet mist
what does camu tuta pel mean?
i don't know
I took the first shit I found on the youtube page
sweet mist
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grand wedge
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