Math Challenge - Can you find an arithmetic progression whose first six terms are prime numbers?

A small example: 7, 37, 67, 97, 127, 157.

My website http://users.cybercity.dk/~dsl522332/math/cpap.htm... shows the first case with 6 consecutive primes:

121174811 + 30n, n=0..5

Another page http://users.cybercity.dk/~dsl522332/math/aprecord... shows the record 26 primes in arithmetic progression.

T1 = a T2 = a + d T11 = a + 10d T 12 = a + 11d considering the fact that each and each even words is d better than ordinary term till now it, then T2 + T4 + ... + T12 = T1 + T3 + ... + T11 + 6d seventy 8 = 60 + 6d d = 3 notice that T1, T3, ..., T11 and T2, T4, ..., T12 additionally are arithmetic progressions so we are able to apply here formula for sum: S = n (first term + final term) / 2 S(ordinary) = 60 6 (T1 + T11) / 2 = 60 3 (a + a + 10d) = 60 (2a + 30) = 20 2a = ?10 a = ?5 S(even) = seventy 8 6 (T2 + T12) / 2 = seventy 8 3 (a + d + a + 11d) = seventy 8 (2a + 36) = 26 2a = ?10 a = ?5 a = ?5 d = 3 twelfth term = ?5 + 11(3) = 28

5, 11, 17, 23, 29,

31, 37, 43,

41, 47, 53, 59

601, 607, 613, 619,

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