Block #2,664,436

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.

3.742 × 10⁹⁷(98-digit number)

37429406941519919095…92705432776487485439

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

3.742 × 10⁹⁷(98-digit number)

37429406941519919095…92705432776487485439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.485 × 10⁹⁷(98-digit number)

74858813883039838190…85410865552974970879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.497 × 10⁹⁸(99-digit number)

14971762776607967638…70821731105949941759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.994 × 10⁹⁸(99-digit number)

29943525553215935276…41643462211899883519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.988 × 10⁹⁸(99-digit number)

59887051106431870552…83286924423799767039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.197 × 10⁹⁹(100-digit number)

11977410221286374110…66573848847599534079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.395 × 10⁹⁹(100-digit number)

23954820442572748221…33147697695199068159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.790 × 10⁹⁹(100-digit number)

47909640885145496442…66295395390398136319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.581 × 10⁹⁹(100-digit number)

95819281770290992884…32590790780796272639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.916 × 10¹⁰⁰(101-digit number)

19163856354058198576…65181581561592545279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

3.832 × 10¹⁰⁰(101-digit number)

38327712708116397153…30363163123185090559

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 #2,664,436

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