Block #442,002

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/13/2014, 12:52:25 PM · Difficulty 10.3503 · 6,354,899 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cc5eaf3ebec66e145565a6b77212122e3f60930a13f4c1b1da917ae62c337e2f

View on Chainz ↗

Height

#442,002

Difficulty

10.350254

Transactions

Size

395 B

Version

Bits

0a59aa3d

Nonce

52,443

Timestamp

3/13/2014, 12:52:25 PM

Confirmations

6,354,899

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

dbb3638b5c24a030a66a47be089dc6726d27c207a57c5ec8d27bf475978a2720

Transactions (2)

Coinbasea2c3cdc3dcbb7f…7818515857c466

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

ea245d434850b0…7d8222163fbdb4

1 in → 1 out1.9921 XPM192 B

AcMdZXM2…MRf2mBpL

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.

1.550 × 10¹⁰²(103-digit number)

15505082370007872006…02609935713961482239

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

1.550 × 10¹⁰²(103-digit number)

15505082370007872006…02609935713961482239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.101 × 10¹⁰²(103-digit number)

31010164740015744012…05219871427922964479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.202 × 10¹⁰²(103-digit number)

62020329480031488025…10439742855845928959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.240 × 10¹⁰³(104-digit number)

12404065896006297605…20879485711691857919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.480 × 10¹⁰³(104-digit number)

24808131792012595210…41758971423383715839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.961 × 10¹⁰³(104-digit number)

49616263584025190420…83517942846767431679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.923 × 10¹⁰³(104-digit number)

99232527168050380840…67035885693534863359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.984 × 10¹⁰⁴(105-digit number)

19846505433610076168…34071771387069726719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.969 × 10¹⁰⁴(105-digit number)

39693010867220152336…68143542774139453439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.938 × 10¹⁰⁴(105-digit number)

79386021734440304672…36287085548278906879

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