He was born three minutes after midnight (2200 GMT) in the maternity ward of the University Clinical Centre.
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Mother and baby were both said to be well.
"It is very fortunate and a pleasure for the entire staff of the clinic ... for this event to happen here," Dr Bukvic said.
UN officials insist that Mr Annan's presence in the Bosnian capital as part of a two-day Balkan tour is purely coincidental and there is no particular reason why Sarajevo was selected.
Had the secretary general been in New York, they say, then a New York baby would have been chosen.
![[ image: width=150]](/olmedia/470000/images/_471908_annan150.jpg)
But the decision to honour a baby from a city still rebuilding itself after Bosnia's bitter war is certain to carry with it an added symbolism.
The move itself is purely symbolic as, with three babies born every single second, no one can pinpoint exactly where and when the key birth might happen.
In any case, most demographers agree the baby is more likely to be born in Asia than Bosnia.
And baby number six billion could also have arrived much earlier, China says.
"Without taking effective measures to slow down the rapid growth of its population, China would have 300 million people more than the current figure of 1.248 billion," senior family planning official Zhang Weiqing was quoted as saying by the official Chinese newsagency.
China operates a one-child policy which has earned it praise and vitriol in almost equal measure.
UN population experts say the country has made sacrifices for the benefit of the whole world.
Human rights groups claim the policy infringes civil liberties and encourages forced abortions.
China denies this, although it admits that occasionally local officials overstep the line.
(Click here to see a graph of world population growth)
Mr Annan is in Sarajevo for talks with Bosnia's multi-ethnic presidency during which they will discuss a proposal to build a memorial to UN personnel involved in bringing peace to the country.
In September, the UN decreed that the day the world's population hits six billion - a day known as D6B - would be 12 October, although officials admit the date is little more than a good guess.
Although the growth rate has slowed in recent years, the world population has doubled since 1960 and the UN estimates that the vast majority of new-born infants will grow up to be poor and illiterate.
Since 1987, global population has increased by a billion and the UN estimates that it will reach 8.9 billion by 2050.
Some population experts argue that a one-child policy, similar to that operating in China, should be adopted worldwide. But others say science will help feed a growing world, and that birth rates are starting to level off.
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Bangladesh running out of space
(11 Oct 99 | South Asia)
UN Population Fund
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Microsoft trial mediator appointed
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![[ image: width=150]](/olmedia/470000/images/_471908_flats150.jpg)
![[ image: width=300]](/olmedia/450000/images/_454509_world_population.gif)
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