- 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

just these 3 additions.

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] - At 12:15 PM 6/9/2005, Milton Brown wrote:

>All twin primes can be constructed by

Wrong, because you don't have any limit on f, nor say what f will work for

>

>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.

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. - At 12:15 PM 6/9/2005, Milton Brown wrote:

>All twin primes can be constructed by

Can you outline your construction procedure? Also, take p=2^24036583-1 and

>

>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.

show how you find an f that will work.