## RE Unnecessary Primes

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• And how do you know that there aren t even numbers bigger than 400 that would need 11, 17... as necessary primes for achieve GC? Do you have a proof? If not,
Message 1 of 2 , Apr 6, 2005
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And how do you know that there aren't even numbers bigger than 400 that
would need 11, 17... as necessary primes for achieve GC?

Do you have a proof? If not, how did you come to that claim?

Jose Brox

----- Original Message -----
From: "xeipon2" <ed@...>
Sent: Wednesday, April 06, 2005 6:42 AM

I claim that the following primes are unnecessary for GC.

11, 17, 29, 41, 59, 67, 71, 73, 89, 97, 103, 127, 137, 149, ...

Here are the even numbers up to 400 expressed without these
primes. Can anyone extend the list of Unnecessary Primes --
or perhaps point out some even number where they are necessary?
--Ed Pegg Jr

{4,2,2},{6,3,3},{8,3,5},
{10,3,7},{12,5,7},{14,7,7},{16,3,13},{18,5,13},
{20,7,13},{22,3,19},{24,5,19},{26,3,23},{28,5,23},
{30,7,23},{32,13,19},{34,3,31},{36,5,31},{38,7,31},
{40,3,37},{42,5,37},{44,7,37},{46,3,43},{48,5,43},
{50,3,47},{52,5,47},{54,7,47},{56,3,53},{58,5,53},
{60,7,53},{62,19,43},{64,3,61},{66,5,61},{68,7,61},
{70,23,47},{72,19,53},{74,13,61},{76,23,53},{78,31,47},
{80,19,61},{82,3,79},{84,5,79},{86,3,83},{88,5,83},
{90,7,83},{92,13,79},{94,47,47},{96,13,83},{98,19,79},
{100,47,53},{102,19,83},{104,3,101},{106,5,101},{108,7,101},
{110,3,107},{112,3,109},{114,5,109},{116,3,113},{118,5,113},
{120,7,113},{122,13,109},{124,23,101},{126,13,113},{128,19,109},
{130,23,107},{132,19,113},{134,3,131},{136,5,131},{138,7,131},
{140,31,109},{142,3,139},{144,5,139},{146,7,139},{148,47,101},
{150,19,131},{152,13,139},{154,3,151},{156,5,151},{158,7,151},
{160,3,157},{162,5,157},{164,7,157},{166,3,163},{168,5,163},
{170,3,167},{172,5,167},{174,7,167},{176,3,173},{178,5,173},
{180,7,173},{182,3,179},{184,3,181},{186,5,181},{188,7,181},
{190,23,167},{192,13,179},{194,3,191},{196,3,193},{198,5,193},
{200,3,197},{202,3,199},{204,5,199},{206,7,199},{208,101,107},
{210,13,197},{212,13,199},{214,3,211},{216,5,211},{218,7,211},
{220,23,197},{222,23,199},{224,13,211},{226,3,223},{228,5,223},
{230,3,227},{232,3,229},{234,5,229},{236,3,233},{238,5,233},
{240,7,233},{242,3,239},{244,3,241},{246,5,241},{248,7,241},
{250,23,227},{252,13,239},{254,3,251},{256,5,251},{258,7,251},
{260,3,257},{262,5,257},{264,7,257},{266,3,263},{268,5,263},
{270,7,263},{272,3,269},{274,3,271},{276,5,271},{278,7,271},
{280,3,277},{282,5,277},{284,3,281},{286,3,283},{288,5,283},
{290,7,283},{292,23,269},{294,13,281},{296,3,293},{298,5,293},
{300,7,293},{302,19,283},{304,23,281},{306,13,293},{308,31,277},
{310,3,307},{312,5,307},{314,3,311},{316,3,313},{318,5,313},
{320,3,317},{322,5,317},{324,7,317},{326,13,313},{328,47,281},
{330,13,317},{332,19,313},{334,3,331},{336,5,331},{338,7,331},
{340,3,337},{342,5,337},{344,7,337},{346,53,293},{348,31,317},
{350,3,347},{352,3,349},{354,5,349},{356,3,353},{358,5,353},
{360,7,353},{362,3,359},{364,5,359},{366,7,359},{368,19,349},
{370,3,367},{372,5,367},{374,7,367},{376,3,373},{378,5,373},
{380,7,373},{382,3,379},{384,5,379},{386,3,383},{388,5,383},
{390,7,383},{392,3,389},{394,5,389},{396,7,389},{398,19,379},
{400,3,397}

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• ... I have numerical evidence up to 30000. ... Of course I don t have a proof. :) I m appealing to just numerical evidence. I would be curious to see the
Message 2 of 2 , Apr 6, 2005
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--- Jose Ram�n Brox <ambroxius@...> wrote:
> And how do you know that there aren't even numbers bigger than 400 that
> would need 11, 17... as necessary primes for achieve GC?

I have numerical evidence up to 30000.

> Do you have a proof? If not, how did you come to that claim?
>
> Jose Brox

Of course I don't have a proof. :) I'm appealing to just numerical evidence.
I would be curious to see the Unnecessary primes up to a million or so, perhaps
tested to a billion. Are there any patterns in them? What is their percentage?

I made a list of Unnecessary Triangular numbers for Gauss's tri+tri+tri=x for
any number x a few years back, and thought I would do the same for Prime
numbers and Goldbach's conjecture, just to see if they were already in OEIS.

--Ed Pegg Jr

> From: <ed@...>
> I claim that the following primes are unnecessary for GC.
>
> 11, 17, 29, 41, 59, 67, 71, 73, 89, 97, 103, 127, 137, 149, ...
>
> Here are the even numbers up to 400 expressed without these
> primes. Can anyone extend the list of Unnecessary Primes --
> or perhaps point out some even number where they are necessary?
> --Ed Pegg Jr
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