Block #3,367,212

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.

4.475 × 10⁹⁴(95-digit number)

44755429661309499133…20655534300080411649

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

4.475 × 10⁹⁴(95-digit number)

44755429661309499133…20655534300080411649

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.951 × 10⁹⁴(95-digit number)

89510859322618998267…41311068600160823299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.790 × 10⁹⁵(96-digit number)

17902171864523799653…82622137200321646599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.580 × 10⁹⁵(96-digit number)

35804343729047599306…65244274400643293199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.160 × 10⁹⁵(96-digit number)

71608687458095198613…30488548801286586399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.432 × 10⁹⁶(97-digit number)

14321737491619039722…60977097602573172799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.864 × 10⁹⁶(97-digit number)

28643474983238079445…21954195205146345599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.728 × 10⁹⁶(97-digit number)

57286949966476158890…43908390410292691199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.145 × 10⁹⁷(98-digit number)

11457389993295231778…87816780820585382399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.291 × 10⁹⁷(98-digit number)

22914779986590463556…75633561641170764799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

4.582 × 10⁹⁷(98-digit number)

45829559973180927112…51267123282341529599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #3,367,212

Cookie Preferences