# Prime+30=Prime, Unless answer is prime x's prime?

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Just messing around with primes+30 to give next primes,

some +30's do not equal a prime, but if not, they always equal a prime x's a prime?

when this happens, I add 30 again, which gives a prime, unless it is once again a prime x's a prime.

Example: Prime 19 + 30= 49, not a prime, but a prime x's a prime =7x7=49, but then add 30 again will give me prime 79.

So no prime x's prime can equal a prime?

why does adding 30 to a prime, always give a prime, unless the answer is a prime x's a prime, but adding 30 again gives a prime?

prime plus 30 prime x prime

5 35 5x7 +30=65 = 5x13 +30=95 = 5x19 +30=125=25x5 +30=155 =31x5 +30=185 =19x5

7 37

11 41

13 43

17 47

19 49 7x7 +30=79

23 53

29 59

31 61

37 67

41 71

43 73

47 77 11x7 +30=107

53 83

59 89

61 91 13x7 +30=121 +30=151

67 97

71 101

73 103

79 109

83 113

89 119 17x7 +30=149

97 127

101 131

103 133 19x7 +30=163

107 137

109 139

113 143 13x11 +30=173

127 157

131 161 23x7 +30=191

137 167

139 169 13x13 +30=199

149 179

151 181

157 187 17x11 +30=217 =31x7 +30=247 =19x13 +30=277

163 193

167 197

173 203 29x7 +30=233

179 209 19x11 +30=239

181 211

191 221 17x13 +30=251

193 223

197 227

199 229

211 241

223 253 23x11 +30=283

227 257

229 259 37x7 +30=289= 17x17 +30=329 =47x7 +30=359

233 263

239 269

241 271

251 281

257 287 41x7 +30=317

263 293

2 is prime

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prime plus 30 prime x prime
5 35 5x7 +30=65 = 5x13 +30=95 = 5x19 +30=125=25x5 +30=155 =31x5 +30=185 =19x5

25 is not prime

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some +30's do not equal a prime, but if not, they always equal a prime x's a prime?

All non-primes are the product of primes.

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Strange has definitively answered one of your questions (all numbers are either primes or multiples of primes) this is the Fundamental Theory of Arithmetic

The 30 gap thing is to do with the number system - but it is not that useful or interesting. Think on this and it will become obvious:

1. A prime number must be of the form 2w+1 (it must be odd (apart from 2 itself)

2. At the same time the prime must be of the form 3y+1 or 3y+2 (it cannot be divided by 3)

3. Still at the same time the prime must be of the form 5z+1, 5z+2, 5z+3, or 5z+4 (it cannot be divided by 5)

4. This pattern continues with 7, 9 ,11 ,13 etc as the prime grows

5. 30 is 2 x 3 x 5

6. So, if you already have a prime you are adding a simple multiple of 2s, 3s, and 5s to the prime

7. As an example (2w+1) + (2 x 3 x 5) = 2w+1 + 2 x 15 = 2(w+15) + 1 (ie still cannot be divided by 2)

8. This follows for 3 and for 5

9. In short - any number not divisible by 2 ,3 or 5 will when 30 is added still not be divisible

You will notice your +30 schema fails as soon as 7s start cropping up. (+210 will work too - but less often)

The reason that adding 30 again often gives a prime is that 30 is NOT divisible by any prime greater than 5. So you can know that if your (failed selection) is, for example divisible by 11, then (failed selection +30) CANNOT be divisible by 11.

Sooner or later adding 30 a second time will not work, but a third or fourth might. But hopefully you can see that this is not predictive of primes - or it is selectively predictive - but it is kinda obvious when you look at how numbers are made up and not useful because you still have to check

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2 is prime

Yep:),But...,I found it seemed to work after 5, but 2 & 5 would still give me all prime x primes of 2 & 5: 2 x31 5x5 etc.

@strange @Imatfaal, Thanks for info, did not fully realize(understand) about unique-prime-factorization theorem, &"composite numbers" where the plus 30 fails 35,49,77 etc,

I just found it interesting,that these composite numbers are the product of just "2 primes" that went to a sort of order, 5x7 7x7, 11x7, 13x7, etc, so has i went higher up the primes, I would use 7 & every other prime 7x103, 7x113, 7x131etc.

Then 11 and every other prime,

Then 13 and ever other prime, etc.

But then again it does help if you know your "prime x's tables". cheers anyway, back to drawing board.

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Yep:),But...,I found it seemed to work after 5, but 2 & 5 would still give me all prime x primes of 2 & 5: 2 x31 5x5 etc.

@strange @Imatfaal, Thanks for info, did not fully realize(understand) about unique-prime-factorization theorem, &"composite numbers" where the plus 30 fails 35,49,77 etc,

I just found it interesting,that these composite numbers are the product of just "2 primes" that went to a sort of order, 5x7 7x7, 11x7, 13x7, etc, so has i went higher up the primes, I would use 7 & every other prime 7x103, 7x113, 7x131etc.

Then 11 and every other prime,

Then 13 and ever other prime, etc.

But then again it does help if you know your "prime x's tables". cheers anyway, back to drawing board.

I believe primes have fascinated mathematicians since the time whereof the memory of man knoweth not - they are slippery customers and every time we (even great mathematical colossi) think they have a good handle on them they squirm free. We know a huge amount about them and about factorization - but the holes in our knowledge are annoying and not insignificant.

The Mathematical communities main avenue of approach is via the Riemman Zeta function - but that is really gnarly maths

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I believe primes have fascinated mathematicians since the time whereof the memory of man knoweth not - they are slippery customers and every time we (even great mathematical colossi) think they have a good handle on them they squirm free. We know a huge amount about them and about factorization - but the holes in our knowledge are annoying and not insignificant.

The Mathematical communities main avenue of approach is via the Riemman Zeta function - but that is really gnarly maths

Personally, I always found Stanisław Ulam's discovery of the correlation between primes and geometry very fascinating.

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Personally, I always found Stanisław Ulam's discovery of the correlation between primes and geometry very fascinating.

A truly great mathematician - in an age in which the competition was tough.

There was such a flourishing of mathematical/scientific genius in the 30s and 40s - and it is such a tragedy that the world was forced / allowed itself to use that brilliance to develop weapons. Where would we be as a species if the incredible genius of people like Ulam and the other colossal intellects of the Manhattan project has been free to choose their own goals - yet were still granted the resources, the time, and the ambition and ability to work together.

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A truly great mathematician - in an age in which the competition was tough.

There was such a flourishing of mathematical/scientific genius in the 30s and 40s - and it is such a tragedy that the world was forced / allowed itself to use that brilliance to develop weapons. Where would we be as a species if the incredible genius of people like Ulam and the other colossal intellects of the Manhattan project has been free to choose their own goals - yet were still granted the resources, the time, and the ambition and ability to work together.

I don't think it's possible at least not for a long time but that is a kind of utopia that I would love to live in.

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