Primes, and products of primes

I was finding it difficult to stop thinking and fall asleep last night, so I decided to count as far as I could, in primes or products of primes. I'm not sure why, but it did stop the thoughts whirling around like a hamster on a wheel.

Note on superscripts: HTML only allows me to show squares and cubes. Do the addition.

1
2
3
2²
5
2×3
7
2³
3²
2×5
11
2×3²
13
2x7
3x5
2²×2²
17
2×3²
19
2²×5
3×7
2×11
23
2³×3
5²
2×13
3³
2²×7
29
2×3×5
31
2²×2³
3×11
2×17
5×7
2²×3²
37
2×19
3×13
2³×5
41
2×3×7
43
2²×11
3²×5
2×23
47
2²×2²×3
7²
2×5²
3×17
2²×13
53
2×3³
5×11
2³×7
3×19
2×29
59
2²×3×5
61
2×31
2×3×11
2³×2³
5×13
2×3×11
67
2²×17
3×23
2×5×7
71
2³×3² 
73
2×37
3×5²
2²×19
7×11
2×3×13
79
2²×2²×5
3²×3²
2×41
83
2²×3×7
5×17
2×43
3×29
2³×11
89
2×3³×5
7×13
2²×23
3×31
2×47
5×19
2²×2³×3
97
2×7²
3²×11
2²×5²
101

Please comment if I got the coding or arithmetic wrong! It's been fun to figure all this out -- in my head if I could, on paper if I had to.