BGP without default route

I have a scenario below and my question is why do I need the default route site1 and site2 router so that they can ping each other. Without the default route, I can see network 172.31.1.0/24 via 10.10.10.1 from router site2. But why I cannot ping 172.31.1.1.

net diagram
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leblancAccountingAsked:
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giltjrCommented:
From what subnet are you ping'ing?

What do you mean you can "see 172.31.1.0/24 via 10.10.10.1"?

To get to a host that is not on the same subnet, each L3 device must know who to route the request through.  Without a default route, you would need a specific route.  Without a specific route or a default route a device has no idea who to route the request through, so it just drops the packet.
mikebernhardtCommented:
You need to have some kind of IGP (static route, OSPF, something) to get between the LAN routers and the Site routers. Even if you are running iBGP between them. And unless you have a number of static routes pointing to the other site, you need a default route on the LAN routers  for the LAN routers to know where to go for external routes.
leblancAccountingAuthor Commented:
"What do you mean you can "see 172.31.1.0/24 via 10.10.10.1"?" The sh ip ro from site2 router shows that there is a route to 172.31.1.0 via 10,10,10,1. But I cannot ping 172.31.1.1.

site2 router (without the default gateway):
site2#sh ip ro
Codes: C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2
       i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
       ia - IS-IS inter area, * - candidate default, U - per-user static route
       o - ODR, P - periodic downloaded static route

Gateway of last resort is not set

     172.31.0.0/24 is subnetted, 1 subnets
B       172.31.1.0 [20/0] via 10.10.10.1, 00:00:52
     10.0.0.0/8 is variably subnetted, 2 subnets, 2 masks
C       10.10.10.0/30 is directly connected, FastEthernet1/0
C       10.10.255.2/32 is directly connected, Loopback0
C    192.168.1.0/24 is directly connected, FastEthernet0/0

The lan routers are actually switches. But I did not turned them on yet.
giltjrCommented:
O.K., SITE2 router has received a route via BGP that says go get to 172.31.1.0/24 go to 10.10.10.1.

I would assume that 10.10.10.1 (MPLS2) 10.10.10.1 has a route that says to get to 172.31.1.0/24 go to 10.10.10.6.

Then 10.10.10.6 (SITE1 router) is attached to 172.31.1.0/24, so it knows how to get there.

Now you need to look at the routes going back.  That is, does SITE1 router have a default route that points to 10.10.10.5 or does it have some other route that points to the subnet you are on that points to 10.10.10.5.  Does MPLS2 have a route that points back to your IP address.

Last, but not least, could something be configured to drop/reject ICMP packets along the way.

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