- 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@...>

To: <primenumbers@yahoogroups.com>

Sent: Wednesday, April 06, 2005 6:42 AM

Subject: [PrimeNumbers] Unnecessary Primes

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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Yahoo! Groups Links - --- Jose Ram�n Brox <ambroxius@...> wrote:
> And how do you know that there aren't even numbers bigger than 400 that

I have numerical evidence up to 30000.

> would need 11, 17... as necessary primes for achieve GC?

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

Of course I don't have a proof. :) I'm appealing to just numerical evidence.

>

> Jose Brox

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