Route Card 9 - Interneting

Part 1 - Number Gossip

Start at the beginning of the B[whose number is the earliest even year in which a person must be born, who lives no more than 100 years, in order that she never celebrates a prime birthday in a prime year]

via S? [which is the smallest prime whose sum of digits is square]
via ? [which is the sum of the cubes of the first two primes]
via ? [which is the smallest perfect number]N
via NNE? [which is the number of black keys on a piano]
via ? [which is the smallest non-palindromic prime which on subtracting its reverse gives a perfect cube]E
via ? [which is the smallest number with multiplicative persistence 4]
via ? [which is the only number such that the common alphabetical value of its Roman representation is equal to its reversal] 
via ? [which is the only number such that the common alphabetical value of its Roman representation is equal to its reversal] 
not via ? [which is the smallest multidigit prime consisting of only curved digits]
via NE? [which is the largest Mersenne prime with all different digits]
via ? [which is the only even prime number]
via ? [which is its own factorial, and its own square and cube and so on]
via ? [which is the smallest pandigital number in base 4]N
via ? [which is the multiplicative identity]N

Finish at next junction.

Solving the clues by perhaps predicting the number ad looking up on the Number Gossip website should have given you the following list to plot:
5246 S13 35 6N NNE36 41E 77 67(LXVII - 12+24+22+9+9=76) 67 (83) NE127 2 1 75N 1N

Route Checks
1) T 5
2) R>W 1
3) O>W 1 (missed by many because of the approach S to 13 and shorter O>W route)
4) J-E YYY (not RRO for those that didn't plot the second 67)
5) GS-S 5211

Part 2 - Wikipedia Years

Continue via:

Muryeong becomes king of Baekje (501),
Emperor Huai of Jin died (313),
An earthquake devastates Latakia (494),
Ireland's first city, Waterford, is founded on the River Suir (914),
Seneca the Younger becomes Nero's tutor (49),
Construction of the Antonine Wall is completed (144),
Charles the Bald, Louis the German and Lothar meet in Koblenz (848),
Jima of Silla died (134),
The second Battle of Roncevaux Pass is fought between the Basques and the Franks (812),
First year of Yuanchu era of the Chinese Eastern Han Dynasty (114),
Emperor Basil I of the Byzantine Empire born (811),
Peter the Iberian, Georgian monk died (491),
Empress Liang Na, wife of Emperor Shun of Han died (150),
Roman emperor Domitian born (51),
Godwin, Earl of Wessex returns to England from exile (1052),
Hisham II is restored as Umayyad caliph of Cordoba, succeeding Suleiman II (1010),
Saturnin, Syrian theologian born (53),
The Romans conquer Kerak from the Nabateans (105),
Rabbula becomes bishop of Edessa (411),
King Sigurd II of Norway died (1155),
Illyria is divided into Pannonia and Dalmatia (10),
Hou Zhu succeeds Wu Cheng Di as ruler of the Chinese Northern Qi Dynasty (565),
Birth of Lai Ji (610).

Finish at next junction.

Reference to Wikipedia should have given you the following sequence:
501 313 494 914 49 144 848 134 812 114 811 491 150 51 1052 1010 53 105 411 1155 10 565 610
There were a few differing dates in Wikipedia but only ever one plotable alternative.

which you punctuate to grid line crossings thus:
50 13 13 49 49 14 49 14 48 48 13 48 12 11 48 11 49 11 50 51 10 52 10 10 53 10 54 11 11 55 10 56 56 10

Route Checks
6) ETL 2
7) RO 2
8) G>W 2
9) Ch+ 3/4 (2 in 5209, 1 in 5509, a marginal one in 5610)
10) Finish Grid Square 5510