Block #412,946

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/20/2014, 9:10:32 PM · Difficulty 10.4195 · 6,383,595 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

b6419577a7ae8d84205ff1ef1c6d36d7d3b21fe5d31a648da7c585d430bdf8ea

View on Chainz ↗

Height

#412,946

Difficulty

10.419495

Transactions

Size

900 B

Version

Bits

0a6b6403

Nonce

245,468

Timestamp

2/20/2014, 9:10:32 PM

Confirmations

6,383,595

Mined by

⛏️ MaSn2AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

10caa9cd35e2201edb7f58bfd28c430f1bd719223de075d5ae9bce2f04ec059e

Transactions (1)

Coinbase10caa9cd35e220…9bce2f04ec059e

1 in → 22 out9.2000 XPM811 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AQwRN8bE…V8PsTcY9

Prime Chain Origin

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.

5.898 × 10⁹²(93-digit number)

58982168175066918438…90406324329099847679

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

5.898 × 10⁹²(93-digit number)

58982168175066918438…90406324329099847679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.179 × 10⁹³(94-digit number)

11796433635013383687…80812648658199695359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.359 × 10⁹³(94-digit number)

23592867270026767375…61625297316399390719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.718 × 10⁹³(94-digit number)

47185734540053534750…23250594632798781439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.437 × 10⁹³(94-digit number)

94371469080107069501…46501189265597562879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.887 × 10⁹⁴(95-digit number)

18874293816021413900…93002378531195125759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.774 × 10⁹⁴(95-digit number)

37748587632042827800…86004757062390251519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.549 × 10⁹⁴(95-digit number)

75497175264085655601…72009514124780503039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.509 × 10⁹⁵(96-digit number)

15099435052817131120…44019028249561006079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.019 × 10⁹⁵(96-digit number)

30198870105634262240…88038056499122012159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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