## Building Twin Primes III

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• All twin primes can be constructed by 30*P +(11,13) or +(17,19) or +(29,31) or 30*P + 30f +(11,13) or +(17,19) or +(29,31) where P is a prime and f is a
Message 1 of 3 , Jun 9, 2005
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All twin primes can be constructed by

30*P +(11,13) or +(17,19) or +(29,31) or

30*P + 30f +(11,13) or +(17,19) or +(29,31)

where P is a prime and f is a fudge-factor,
very small 1, 3 or 4.

This allows all primes to be associated with a
higher Twin Prime, and since the sequence

2, 3, 5, ..., P, ... is infinite,

the number of Twin Primes is infinite.

The first few Twin Prime can all be constructed with
30*k + (11,13) or +(17,19) or +(29,31). After that the
Twin Primes can be constructed with previously built
smaller Twin Primes. Many can still be constructed with

Attached is a table for k from 1 to 20 and some
higher primes showing their construction.
This is followed by the construction
of more Twin Primes from primes and
previous Twin Primes.

The assertion is that for every k which is prime,
there is at least smaller twin prime (already produced)
which produces a new twin prime.

(30)k---+(11,13) -------+(17,19) ------+(29,31)
================================================
1 -------(41,43) --------xxxxxxxx------- (59,61)
2p ------(71,73) --------xxxxxxxx -------xxxxxxx
3p ------(101,103) ------(107,109) ------xxxxxxx
4 -------xxxxxxxxxx -----(137,139) ------(149,151)
5p ------xxxxxxxxxx -----xxxxxxxxxx -----(179,181)

6 -------(191,193) ------(197,199) ------xxxxxxxxx
7p ------xxxxxxxxxx -----(227,229) ------(239,241)
8 -------xxxxxxxxxx -----xxxxxxxxxx -----(269,271)
9 -------(281,283) ------xxxxxxxxxxx ----xxxxxxxxx
10 ------(311,313) ------xxxxxxxxxx -----xxxxxxxxx

11p -----xxxxxxxxxxx ----(347,349) ------xxxxxxxxx
12 ------xxxxxxxxxx -----xxxxxxxxxx -----xxxxxxxxx
13p -----xxxxxxxxxx -----xxxxxxxxxx -----(419,421)
14 ------(431,433) ------xxxxxxxxxx -----xxxxxxxxx
15 ------(461,463) ------xxxxxxxxxx -----xxxxxxxxx

16 ------xxxxxxxxxx -----xxxxxxxxxx -----xxxxxxxxx
17p -----(521,523) ------xxxxxxxxxx -----xxxxxxxxx
18 ------xxxxxxxxxxx ----xxxxxxxxxx -----(569,571)
19p -----xxxxxxxxxxx ----xxxxxxxxxx -----(599,601)
20 ------xxxxxxxxxx -----(617,619) ------xxxxxxxxx

23 ------690-----(827,829)------ +(137,139)--{27*30+(17,19)}
+4

29 ------870-----(881,883)------ +(11,13)

31-------930-----(1031,1033)---- +(101,103)--{34*30+(11,13)}
+3

37 ------1110 ---(1151,1153) ----+(41,43)----{38*30+(11,13)}
+1

41-------1230----(1289,1291) ----+(59,61)----{42*30+(29,31)}
+1

43 ------1290----(1301,1303)-----+(11,13)

47-------1410----(1427,1429) ----+(17,19)

51-------1530----(1667,1669) ----+(137,139)--{55*30+(17,19)}
+4

53-------1590----(1607,1609) ----+(107,109)--{56*30+(17,19)}
+3

59-------1770----(1787,1789) ----+(17,19)

61-------1830----(1871,1873) ----+(41,43)----{62*30+(11,13)}
+1

67-------2010----(2027,2029) ----+(17,19)

71-------2130----(2141,2143) ----+(11,13)

73-------2190----(2339,2341) ----+(149,151)--{77*30+(29,31)}
+4

79-------2370----(2381,2383) ----+(11,13)

83-------2490----(2549,2551) ----+(59,61)----{84*30+(29,31)}
+1

89-------2670----(2687,2689) ----+(17,19)

97-------2910----(2969,2971) ----+(59,61)----{98*30+(29,31)}
+1

101------3030----(3167,3169) ----+(137,139)--{105*30+(17,19)}
+4

103------3090----(3119,3121) ----+(29,31)

107------3210----(3251,3253) ----+(41,43)----{108*30+(11,13)}
+1

109------3270----(3299,3301) ----+(29,31)

113------3390----(3389,3391) ----+(-1,1)

Milton L. Brown

[Non-text portions of this message have been removed]
• ... Wrong, because you don t have any limit on f, nor say what f will work for each P. And if you re going to have that fudge factor in there, basically (P+f)
Message 2 of 3 , Jun 10, 2005
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At 12:15 PM 6/9/2005, Milton Brown wrote:

>All twin primes can be constructed by
>
>30*P +(11,13) or +(17,19) or +(29,31) or
>
>30*P + 30f +(11,13) or +(17,19) or +(29,31)
>
>where P is a prime and f is a fudge-factor,
>very small 1, 3 or 4.
>
>This allows all primes to be associated with a
>higher Twin Prime, and since the sequence
>
>2, 3, 5, ..., P, ... is infinite,
>
>the number of Twin Primes is infinite.

Wrong, because you don't have any limit on f, nor say what f will work for
each P.
And if you're going to have that fudge factor in there, basically (P+f)
where f is whatever you need it to be, then there is really no need for
P. And you're back to square one.
• ... Can you outline your construction procedure? Also, take p=2^24036583-1 and show how you find an f that will work.
Message 3 of 3 , Jun 11, 2005
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At 12:15 PM 6/9/2005, Milton Brown wrote:

>All twin primes can be constructed by
>
>30*P +(11,13) or +(17,19) or +(29,31) or
>
>30*P + 30f +(11,13) or +(17,19) or +(29,31)
>
>where P is a prime and f is a fudge-factor,
>very small 1, 3 or 4.

Can you outline your construction procedure? Also, take p=2^24036583-1 and
show how you find an f that will work.
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