Challenge question: Number sequences!?

[lithiumdeuteride]

Here are some number sequences I thought up. See if you can find the next number, and also identify the pattern.

Sequence 1:
1, 3, 4, 7, 6, 12, 8, 15, 13, ?

Sequence 2:
100, 19, 83, 34, 70, 45, ?

Sequence 3:
1, 1, 0, -1, 0, 7, 28, 79, 192, ?

Sequence 4:
2, 5, 10, 17, 28, 41, 58, 77, 100, ?

The numbers in the sequence may or may not depend on the previous number.

[tsr21]

S2: 61
S4: 129
S1: 18
S3: 431

[kyle]

Sequence 4
Next term would be 129

The formula is a[n+1] = a[n] + p[n], where p is the set of all prime numbers