Why does Ellie see these pulses as a sign of intelligent life or what is the significant about the number of pulses?

Contact

If you could send a long message to such extraterrestrial beings - words, pictures, sounds, music - what would you say? How would you describe us? What would you leave out? Could you communicate intelligibly to very different beings with a wholly independent evolution? In 1977, at NASA's behest, a few of us had a remarkable opportunity to attempt such a (one-way) communication. Frank Drake suggested not a plaque, but a phonograph record. As described in the book, Murmurs of Earth, we designed and prepared the record to carry a rich message to the stars - 116 pictures and diagrams about our global civilization and our species, greetings, samples of the world's great music, the brain waves of a young woman in love and much else.
Carl Sagan and Ann Druyan from the Carl Sagan Portal at http://www.carlsagan.com/

Dr. Carl Sagan devoted his life to research on the origin of life and the search for life and intelligence elsewhere in the cosmos. His novel, Contact, and the movie by the same name follow the adventures of Dr. Ellie Arroway as she monitors radio telescope feedback in her work for the Search for Extra-Terrestrial Intelligence, or SETI. One night, as the radio telescopes are pointed toward Vega, Ellie discovers some strange pulses through the background noise:

Two pulses followed by a pause

Three pulses followed by a pause

Five pulses followed by a pause

Seven pulses followed by a pause

Eleven pulses followed by a pause

Thirteen pulses followed by a pause

Seventeen pulses followed by a pause

Nineteen pulses followed by a pause

Twenty-three pulses followed by a pause

Twenty-nine pulses followed by a pause

The pattern continues through ninety-seven pulses followed by a pause and then repeats. Ellie is convinced that only intelligent life could generate the structure in the sequence of pulses. "It's hard to imagine some radiating plasma sending out a regular set of mathematical signals like this."