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1. Its capital is on the Atlantic coast
Libreville is an Atlantic city, Lima is a Pacific city.
Gabon
Peru
2. Its official name in English is "Republic of __________"
Gabonese Republic ("République gabonaise") vs. Republic of Peru ("República del Peru")
Gabon
Peru
3. Its most-used language is Spanish
Gabon: French; Peru: Spanish
Gabon
Peru
4. It does not touch the equator
Peru comes within 5km of the equator, but does not touch it.
Gabon
Peru
5. It is in the southern half of its continent (South America vs. Africa)
Taking measurements from the extreme north of Colombia to the extreme south of Chile, Peru is in the northern half of South America. In the same way, Tunisia - South Africa, Gabon is [just] entirely in the southern half.
8. It shares a currency with neighbouring countries
Gabon uses the Central African Franc, along with Cameroon, C.A.R., Chad, R.O.C. and Equatorial Guinea. Peru uses its own currency, the Sol.
Gabon
Peru
9. It has had a citizen serve as UN Secretary General
Peruvian Javier Pérez de Cuéllar served as UN Secretary General 1982-1991.
Gabon
Peru
10. It has a higher GDP per capita
Gabon: $19,252; Peru: $13,410
Gabon
Peru
11. It has more forest coverage (% of area)
Gabon: 89.3%; Peru: ≈60% (not easy to calculate, but pretty clear that Gabon is "ahead")
Gabon
Peru
12. Its flag has horizontal stripes
Gabon: horizontal green, yellow, blue stripes; Peru: vertical red and white stripes
Gabon
Peru
13. It has a higher population density
Gabon: 8/km squared; Peru: 24/km squared
Gabon
Peru
14. Its exports are dominated by petroleum
Peru's exports are dominated by metal ore, although petroleum is also a major part. Gabon's exports are massively dominated by petroleum.
Gabon
Peru
15. Its capital city is closer to Tokyo
Libreville-Tokyo: Cross Africa, cross the Arabian Sea, cross India & China, then cross the sea to get to Japan. It is still a shorter distance than Lima-Tokyo, crossing the Pacific ocean.
Haha, well I started with Peru because I live there and my imagination isn't all that enormous, but Gabon? Hard to say, I wanted a country that was as different as possible without being ridiculously different, if that makes sense.