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University Don Unveils  Mathematical Discovery on  ‘Count of Odd Composites up to Natural Number’

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From Attah Ede, Makurdi

Benue State University (BSU) Makurdi Lecturer, Dr Michael Vershima Atovigba, an Associate Professor on Wednesday, at the university’s Science and Mathematics Education Laboratory, demonstrated his findings for the determination of all odd composites up to a natural number, N.

The work is titled: Odd Composites Algorithm and the K-C Prime Number Equation: An Equation of Total Count of Primes under or up to a Natural Number, N.

Atovigba is famous for his works on Riemann Hypothesis, which was listed in 2001 by the Clay Mathematics Institute, New Jersey, as one of the seven millennium problems, George Akume Precision Equation, a second degree polynomial precision equation useful in economic theory in terms of budgeting and efficient allocation of resources, use of geometry to prove the probability theorem, which stopped the global campaign by America’s Prof.

Gabriel Oyibo, to expunge probability from the world university curriculum.

Concerned that prime counting functions are approximations rather than precise algorithms that lead to precise counts of total number of primes up to a natural number, Dr. Atovigba says he devoted 15 years, “to search out for more algorithms that might provide with greater precision the total number of primes up to a given natural number.”

His focus therefore, was to establish “a prime number equation which provides total count of primes up to or under a given natural number,” the breakthrough he demonstrated today. The results of his “study have sequence of odd numbers leading to the sequence of odd composites divisible by one or more primes thus further leading to removal of all odd composites divisible by the primes under or up to a natural number, which leaves total number of primes under or up to that natural number.”

Dr. Atovigba’s Theorem, known as Odd Composites Algorithm states that 

C = Sum of (P1) – Sum of (P1,P2) + Sum of (P1,P2,P3) – …

Where

C means algorithm of odd composites

(P1) Means cardinality or count of odd composites divisible by P1 under N (given natural number)

(P1,P2) Means cardinality of odd composites divisible by both P1 and P2

(P1,P2,P3) Means cardinality of odd composites divisible by P1,P2,P3 etc. provided that the product (P1P2P3) etc is less than or equal to N.

In arriving at the equation, Don Atovigba made use of the inclusion-exclusion principle as a method of his study. “The study retains the original prime number equation Eta=K-C (Atovigba, 2014), where K is total number of odd numbers and C, algorithm of odd composites up to a natural number.

His conclusion is that the study has successfully come up with the algorithm for total count of odd composites up to a Natural Number, N, with a computer programme, set for an automation of total count of odd composites, hence total number of primes up to a natural number, using Eta= K-C.

Dr. Atovigba, therefore, recommends that the odd composites algorithm of this study along with the prime number equation should be accepted as platonic objects in number theory, and adopted by schools and universities globally.

“By Platonic object it is meant, the object has all along being in existence and can only be discovered,” he concludes. 

Prior to the breakthrough, Dr. Atovigba, in 2014, proposed the prime number equation (Eta= K-C), to the effect that the total number of primes under or up to a natural number is the difference between count of odd numbers and count of odd composites.

Professor Iormem Kyereve, who chaired the session described it as interesting, especially that primes are useful for rhe determination of the “power of computers.”

While congratulating Dr. Atovigba on the record, Prof Omenka Jerry, Head, Department of Science and Mathematics Education said the work is significant to the advancement of numerical analysis and number theory.

In his words of encouragement, Dr. Alfred Tyav of the Department of Industrial Technology, noted that great men (like Dr. Atovigba) may not be recognised when alive but when they are no more, they are honoured through their works because they have their names written in books of history.

For details of the work, contact Dr. Michael Vershima Atovigba: mikeatovigba@gmail.commatovigba@bsum.org.edu

Education

How female Medicine Degree Holder Abandoned Certificate for Carpentry- Bugaje

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The Executive Secretary, National Board for Technical Education (NBTE), Prof. Idris Bugaje has expressed the need to promote inclusivity, especially for women and persons with disabilities in technical education.

Bugaje stated this in Abuja while assessing the impact of President Bola Tinubu’s administration after two years in office.

He appealed for greater gender inclusivity in vocational and technical education, stressing that deliberate policies such as scholarships and incentives could help bridge the gender gap.

In support of his position, Bugaje shared an inspiring story of a female medical doctor who abandoned her medical career to pursue carpentry.

“There is a story I want to share with you, about a girl who was interested in becoming a carpenter.

“The father was a carpenter and they were four children in the family, three boys and herself.

“Whenever she joined the boys to the workshop, the father would send her away, saying, `you are a girl, go back to the house, you are not supposed to be a carpenter’’.

“Without giving considerations to the passion of the young girl, the father sent her to a medical school.

“She graduated with the MBBS, went and did the one-year internship after graduation, and chose a role as a medical doctor.

“After that, she came back to the father, returned the MBBS certificate to him, and thanked him.

“Afterward, she told the father that her passion is in carpentry, not to practice as medical doctor,” Bugaje narrated

He added that after spending seven years on medical training, the father had no option but to send her to Turkey to learn how to make furniture.

Addressing cultural and societal barriers often faced by young women in technical fields, Bugaje appealed to parents to support their daughters’ interests in trades like plumbing, electrical installation, and carpentry.

He also called on policymakers to prioritise passion and skill development among youth, especially girls, noting that such encouragement could lead to greater innovation and self-reliance.

“If they want to become carpenters, ICT experts, or POP artists, allow them.

“In skills’ training, passion is very important. That’s what motivates children and helps them innovate.

“We need to harness these innovations if the country is to move forward and rise beyond being a third-world nation,” he said.

He emphasized the need to have deliberate policies to encourage women to come into TVET through scholarships and other incentives. (NAN)

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Education

WAEC Apologies for Conducting English Exam Late, Cites Leakage  Prevention

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The West African Examinations Council (WAEC) has apologized for delay in conducting  English Language Paper 2 in the ongoing 2025 West African Senior School Certificate Examination (WASSCE).

 The took place on Wednesday evening.

In a statement by Moyosola Adesina, Acting Head of Public Affairs Department of
WAEC, the council said that it encountered challenges.

”While maintaining the integrity and security of our examination, we faced considerable challenges primarily due to our major aim of preventing leakage of any paper.

“We recognise the importance of timely conduct of examinations and the impact of this decision on candidates, their schools and parents, and we sincerely apologise for any inconveniences caused,” WAEC stated.

It said that it successfully achieved its objective but it inadvertently impacted the timeliness and seamless conduct of the examination.

“In spite of our best efforts, we encountered logistical hurdles, security concerns and socio-cultural factors that negatively influenced our operations,” WAEC said.

The council re-affirmed its commitment to upholding the highest standard in examination conduct, and pledged to continue to promote academic excellence. (NAN)

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Education

FG vows full WAEC CBT shift by 2026 – Minister

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The Minister of Education, Dr Tunji Alausa, has reaffirmed the Federal Government’s commitment to fully transitioning to Computer-Based Test (CBT) examinations for the West African Examinations Council (WAEC) and other exam bodies by 2026.

Dr Alausa made this known while monitoring the conduct of WAEC’s CBT examinations in Abuja on Wednesday.

He expressed optimism about Nigeria’s capacity to modernise its examination system and reduce widespread malpractice through digital innovation.

Commending WAEC’s initiative, the minister described the shift from traditional pen-and-paper exams to CBT as a historic and crucial step toward fairness and educational integrity.

“We are working very hard to eliminate fraud in our exam system, and WAEC is taking the lead,” he said.

Highlighting the advantages of CBT, Alausa noted that the system simplified the exam process while significantly curbing cheating.

“We now have clear evidence that when exams are done using technology, the level of fraud is minimised to almost zero,” he stated.

He further lauded WAEC’s internal safeguards, explaining that the CBT system was operated via a secured Local Area Network (LAN), making it “literally impossible” to hack.

According to the minister, by Nov. 2025, all WAEC multiple-choice exams will be conducted using CBT.

He added that essay questions and NECO examinations would follow suit by 2026.

On infrastructure and logistics, particularly in remote areas, Alausa acknowledged the challenges but assured that scalable solutions are in progress.

“Are we going to be ready to provide every single needed infrastructure by November? Absolutely not.

“But as we move into the future, we will be ready. We have to challenge ourselves as government,” he said.

He also addressed concerns over the logistics of conducting multiple exams.

“In WAEC, the average student takes about eight to nine papers.

“They do it over several days. Those are the logistics we, as administrators, have to work through, and we already are,” he explained.

The ongoing WAEC exams, which began on April 24, are scheduled to conclude on June 20, 2025.

A total of 1,973,253 candidates from 23,554 schools are participating. Of this number, 979,228 candidates are male, accounting for 49.63 per cent, while 994,025 candidates are female, making up 50.37 per cent.(NAN)

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