983 is Prime number, from your logic, it should be 983=210*4+143. but 143 is not a Prime number. so your logic is wrong. about buildingprimenumbers HOT 6 CLOSED

977=210x4+137
983=210x4+143
991=210x4+151

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based on below description on https://github.com/zhaohonggang/BuildingPrimeNumbers/blob/master/building%20prime%20number.txt#L68

m is Prefect Composite Number. m=1 x.....x p
n is the next Prefect Composite Number after m. n=m x q = 1 x...x p x q
[q..m] is the set of all primes and products of primes between q and m. The members of [q..m] is unlimited. If a, b, c are in this set, a x a x a..., bxb...., axaxb, axbxcxc…will also in this set

theorem 1: This theorem describes all prime numbers between m and n can be built using this approach
If b is prime, m < b < n, b can be describe as b = k * m + a
1 <=k < q, a < m, a is 1 or belong to [q..m]

as the case of 983,

m is 210 = 2 x 3 x 5 x 7
so p is 7
n is 2310 = 2 x 3 x 5 x 7 x 11
so q is 11

so if b is 983 = 210x4+143 then a is 143 < m

a belong to [q..m] which is not necessary to be a prime, but is the set of all primes and products of primes between q and m.

143 = 11 * 13, it is the product of prime numbers between [11, 210]

So your examples are not breaking my logic...

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In another word, the logic can be used for generating prime numbers from small to big, but cannot be used to determine a smaller prime number from a larger prime number.

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既然合数可以被加入来算素数，那么，为何你的公式
31=30+1
37=30+7
41=30+11
43=30+13
...
53=30+23
59=30+29
这些全部都是尾部加上素数呢（1,7,11,13,23,29）？能不能统一一下算法，把为何去掉合数的判断加上呢？这样别人才不会被前面的算法误导，楼主你说是吧？

from buildingprimenumbers.

For above examples, only the left side should be prime, cannot guarantee for the right side.

It is saying every prime numbers can be represent by using an adding expression, but not saying the numbers in the expression will be prime.

The direction is using add but not subtraction, like 30+11 -> 41, 210x4+11 * 13 -> 983,

Cannot go like 983 - 210x4 = 143, using this way cannot guarantee to get prime, the larger the number to be, the more not prime examples will happen.

It is the math law which is talked about here, not determined by me.

from buildingprimenumbers.

Your suggestion of lacking examples in document were reasonable.

Added more examples, including below,

https://github.com/zhaohonggang/BuildingPrimeNumbers/blob/master/building%20prime%20number.txt#L65

353=210+11x13 (this is an example of using products of primes in [11,30) instead of a single prime for construction, this kind of examples will grow when number getting larger)

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