[seqfan] Consecutive non-decreasing prime gaps

[zak seidov]

     13 consecutive primes 
{6564959561, 6564959563, 6564959567, 6564959573, 6564959579, 6564959587, 6564959603, 6564959623, 6564959657, 6564959699, 6564959749, 6564959831, 6564959927}
with 12 non-decreasing consecutive gaps
{2, 4, 6, 6, 8, 16, 20, 34, 42, 50, 82, 96}.
13 consecutive primes starting with  24040740949 have
12 non-decreasing gaps:
{4, 6, 8, 12, 12, 12, 16, 18, 20, 22, 24, 36}.
Larger/longer such sets?Zak