Block #680,079

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.411 × 10⁹⁶(97-digit number)

54117653951439631128…50271005845599250041

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

5.411 × 10⁹⁶(97-digit number)

54117653951439631128…50271005845599250041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.082 × 10⁹⁷(98-digit number)

10823530790287926225…00542011691198500081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.164 × 10⁹⁷(98-digit number)

21647061580575852451…01084023382397000161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.329 × 10⁹⁷(98-digit number)

43294123161151704903…02168046764794000321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.658 × 10⁹⁷(98-digit number)

86588246322303409806…04336093529588000641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.731 × 10⁹⁸(99-digit number)

17317649264460681961…08672187059176001281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.463 × 10⁹⁸(99-digit number)

34635298528921363922…17344374118352002561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.927 × 10⁹⁸(99-digit number)

69270597057842727844…34688748236704005121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.385 × 10⁹⁹(100-digit number)

13854119411568545568…69377496473408010241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.770 × 10⁹⁹(100-digit number)

27708238823137091137…38754992946816020481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

5.541 × 10⁹⁹(100-digit number)

55416477646274182275…77509985893632040961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

1.108 × 10¹⁰⁰(101-digit number)

11083295529254836455…55019971787264081921

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #680,079

Cookie Preferences