*BUMP*
I found the first multibase 2-11 prime at 49 digits.
1000000010000011110100010001000101001010110111001
p2(11) = 282607273285049 prime
p3(11) = 79778625518755688566231 prime
p4(11) = 79229371832366624481423213889 prime
p5(11) = 3552722774474136829853851572738251 prime
p6(11) = 22452271075192681829172827769361612489 prime
p7(11) = 36703374584162999724319518312214797399919 prime
p8(11) = 22300746527764412640615739824336532064473601 prime
p9(11) = 6362685588945084624279669878873489108009248579 prime
p10(11)= 1000000010000011110100010001000101001010110111001 prime
p11(11)= 97017234237464999090723789551739711663815588649159 prime
p12(11)= 6319748729976991725084799189099955937359448461796289 = 29*217922369999206611209820661693101928874463740061941
It should be the smallest, because I checked all the numbers below, and on the way I found 28 base 2-10 primes including the one allready known:
multibase2-10.txt