The word "bikkurim" derives from "bekhor", the firstborn son. For instance, Reuven was the "bekhor" of Jacob. "Makkat bekhorot", the plague of the firstborn, was the tenth plague which G-d visited on Egypt, and all the firstborn of Egypt died in it.
The rights of the eldest son in the family are called the "bekhora" (birthright), and we know that Esau sold his birthright to Jacob for a mess of pottage. "Hatzagat bekhora" is the premiere performance of a play or opera.
"Ne'um bekhora" is a speaker's maiden speech in a public institution. The fruits that ripen first are called "bikkurim", first fruits, and in Temple times these were brought as an offering on Shavuot.
The Seven Species. Eretz Israel is described in the Torah as being blessed particularly with seven species of fruits of the land: wheat, barley, the vine, the fig, the pomegranate, the olive and the date.
"For the Lord your G-d is bringing you into a good land, a land of brooks of water, of fountains and depths that spring out of valleys and hills: A land of wheat, and barley, and vines, and fig trees, and pomegranates; a land of oil olive, and honey."
The number seven (sheva) is a significant "Jewish" number, with Biblical, Talmudic and Midrashic sources. Shavuot is celebrated seven weeks after Pesach.
Jewish mourners sit "Shiva" (seven days) after the death of a close relative.
There are seven days in the week, and Jewish tradition refers to seven planets.
The seventh year in every cycle of seven years is the Shemitta year, in which the land must rest. The Jubilee is the year that concludes seven cycles of Shemitta years, and Masekhet Shevi'it is the Tractate in the Mishnah in the Order of Zera'im that deals with the laws of Shemitta.
There are also Hebrew expressions and proverbs relating to the number seven:
Mashgi'ah beshev'a 'einayim - he watches carefully (literally: he watches with seven eyes).
Shiv'a Medorei Gehinom - great trouble and suffering (literally: the Seven Departments of Hell).
Kotev "Noah" beshev'a shegiot - a name for someone who spells abominably (literally: makes seven mistakes in a two-letter word).
Lih'yot baraki'a hashevi'i - to be in a seventh heaven.
Shiv'im lashon - seventy tongues - all the languages in the world according to Chazal [Our Sages].