Block #473,660

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/4/2014, 1:47:04 AM · Difficulty 10.4462 · 6,320,585 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a40cc36235ff45152e24caffa57d26a9885d4af2ac8316856d6744f0af6b316c

View on Chainz ↗

Height

#473,660

Difficulty

10.446160

Transactions

Size

1.19 KB

Version

Bits

0a723785

Nonce

12,174

Timestamp

4/4/2014, 1:47:04 AM

Confirmations

6,320,585

Merkle Root

11d18dbc1e35abbab68e158bda60450fccb5f52d612ca3daf205f8d5e820fa02

Transactions (2)

Coinbaseb309120bceb037…abb0ded2394bd6

1 in → 1 out9.1700 XPM110 B

AeKNrjNj…1NEq95Ta

28f8a66de78e51…20f737d75dd9ad

5 in → 12 out39.7783 XPM1022 B

AWq2eEhj…hMy13sEr AdyGqrxf…FJa7LKc6 APkSf5C5…wYwrjSQa AazfaUAJ…WaQjuUwm AZTpkAuM…a7i5sa6o

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.

1.852 × 10⁹¹(92-digit number)

18525940323093118569…17531447156821657919

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

1.852 × 10⁹¹(92-digit number)

18525940323093118569…17531447156821657919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.705 × 10⁹¹(92-digit number)

37051880646186237139…35062894313643315839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.410 × 10⁹¹(92-digit number)

74103761292372474279…70125788627286631679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.482 × 10⁹²(93-digit number)

14820752258474494855…40251577254573263359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.964 × 10⁹²(93-digit number)

29641504516948989711…80503154509146526719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.928 × 10⁹²(93-digit number)

59283009033897979423…61006309018293053439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.185 × 10⁹³(94-digit number)

11856601806779595884…22012618036586106879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.371 × 10⁹³(94-digit number)

23713203613559191769…44025236073172213759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.742 × 10⁹³(94-digit number)

47426407227118383538…88050472146344427519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.485 × 10⁹³(94-digit number)

94852814454236767077…76100944292688855039

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