- not giving up... I took the decision tree out for L

here's the T-Sequence in its most raw form, and it's

more efficient like David Broadhurst wanted. the t-

sequence works, but I couldn't display it before...

I'm only bringing it to you again, because you math

guys have the brains to figure out where it might go

wrong; It must have an L (-) type and one L (+) type.

I noticed that you were able to translate it into the

Pari/GP (language/platform) to check larger numbers.

100 CLS : C = 1

102 DIM A(1001), LT(1), T(1001)

104 FOR N = 3 TO 7919 STEP 2

106 IF N MOD 3 <> 0 AND N MOD 5 <> 0 AND N <> 7 THEN

108 A(0) = N: A(1) = (N + 1) / 2: A(2) = A(1) - 1

110 FOR I = 3 TO 1001 STEP 2

112 IF A(I - 1) < 3 THEN

114 IF A(I - 1) = 2 THEN

116 A(I) = 1: A(I + 1) = 0

118 M = I + 1: I = 1001

120 ELSE

122 A(I) = 0: M = I: I = 1001

124 END IF

126 ELSE

128 IF A(I - 1) MOD 2 = 1 THEN

130 A(I) = A(I - 2) / 2

132 ELSE

134 A(I) = (A(I - 2) + 1) / 2

136 END IF

138 A(I + 1) = A(I) - 1

140 END IF

142 NEXT I

144 D = 0: L = 3: LT(0) = 2: LT(1) = 2

146 WHILE (L < N - 2)

148 T(M) = 2: T(M - 1) = L: T(M - 2) = (T(M - 1) ^ 2 - 2) MOD N

150 IF T(M - 2) < 2 THEN T(M - 2) = T(M - 2) + N

152 K = 0: Z1 = 0: Z2 = 0

154 FOR J = M - 3 TO 0 STEP -1

156 IF A(J) MOD 2 = 1 THEN

158 IF A(J) = A(J + 1) + A(J + 2) THEN K = 0 ELSE K = 1

160 T(J) = (T(J + 1 + K) * T(J + 2 + K) - L) MOD N

162 ELSE

164 T(J) = (T(J + 2) ^ 2 - 2) MOD N

166 END IF

168 IF T(J) < 2 THEN T(J) = T(J) + N

170 NEXT J

172 Z1 = (T(2) ^ 2 - 2) MOD N

174 IF Z1 < 2 THEN Z1 = Z1 + N

176 Z2 = (T(1) ^ 2 - 2) MOD N

178 IF Z2 < 2 THEN Z2 = Z2 + N

180 IF T(0) = L THEN

182 IF Z1 = 2 AND Z2 = T(M - 2) THEN

184 LT(D) = -1

186 ELSE

188 IF Z1 = T(M - 2) AND Z2 = 2 THEN

190 LT(D) = 1

192 END IF

194 END IF

196 ELSE

198 PRINT N; "is composite!": L = N - 2

200 END IF

202 IF LT(0) = -LT(1) THEN

204 PRINT N; "is prime!": L = N - 2: C = C + 1

206 END IF

208 D = 1: L = L + 1

210 WEND

212 ELSE

214 IF N = 3 OR N = 5 OR N = 7 THEN

216 PRINT N; "is prime!": C = C + 1

218 ELSE

220 PRINT N; "is composite!"

222 END IF

224 END IF

226 NEXT N

228 PRINT C

230 END

the only thing that would not make it work according

to the co-authors that want to patent it... is that

it must have [T(M-2) mod N <> 2]; it must have a per-

iod larger than k(p) = 2.

65 lines of code; let me know if you like it... Bill

the maximum L is ever got to for N <= 7919 was L= 17 - --- In primenumbers@yahoogroups.com,

"paulunderwooduk" <paulunderwood@...> wrote:

> > Will you now please admit that your article was indeed sloppy,

Thanks, Paul.

> > since you missed out testing *oodles* of (n,a) pairs, with 7|n,

> > for no justifiable reason, whatsoever.

>

> Guilty as charged. My deduction about 7*N was flawed.

> I did check numbers divisible by 5 or 7 for n<11364001

As official representative of the factor 7,

may I cordially invite you to test (n,a) pairs

with n > 11364001 and 7|n ?

Best regards

David (on behalf of the factor 7)