Block #714,272

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/9/2014, 10:18:28 PM · Difficulty 10.9554 · 6,079,969 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a075b293e95ef666e2eb19c5896a519d052b32a5fb5eac677658bd5d3252f4cf

View on Chainz ↗

Height

#714,272

Difficulty

10.955368

Transactions

Size

733 B

Version

Bits

0af492fe

Nonce

318,227

Timestamp

9/9/2014, 10:18:28 PM

Confirmations

6,079,969

Merkle Root

eb615e62a1fb9639ce801301f4e03514e651c04263bdc154acada950b7fc5404

Transactions (1)

Coinbaseeb615e62a1fb96…ada950b7fc5404

1 in → 17 out8.3200 XPM641 B

AJzWx2VD…j4ZSMit5 APfZjrNu…Wvzt6AFp Ac5sZcdP…kzV4eckG AebWhrRm…K61Qrkws AdnG9gQ7…N9B7mA2p

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.

1.144 × 10⁹⁹(100-digit number)

11440056470158202856…63397377628042344961

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

1.144 × 10⁹⁹(100-digit number)

11440056470158202856…63397377628042344961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.288 × 10⁹⁹(100-digit number)

22880112940316405713…26794755256084689921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.576 × 10⁹⁹(100-digit number)

45760225880632811427…53589510512169379841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.152 × 10⁹⁹(100-digit number)

91520451761265622855…07179021024338759681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.830 × 10¹⁰⁰(101-digit number)

18304090352253124571…14358042048677519361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.660 × 10¹⁰⁰(101-digit number)

36608180704506249142…28716084097355038721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.321 × 10¹⁰⁰(101-digit number)

73216361409012498284…57432168194710077441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.464 × 10¹⁰¹(102-digit number)

14643272281802499656…14864336389420154881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.928 × 10¹⁰¹(102-digit number)

29286544563604999313…29728672778840309761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.857 × 10¹⁰¹(102-digit number)

58573089127209998627…59457345557680619521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.171 × 10¹⁰²(103-digit number)

11714617825441999725…18914691115361239041

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer