Block #102,693

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/7/2013, 5:56:17 AM · Difficulty 9.5032 · 6,707,008 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7e8c33dc0171bd480cbf862d3f5908fbf24ea2ef6059faa236f1159fcb51b115

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Height

#102,693

Difficulty

9.503223

Transactions

Size

208 B

Version

Bits

0980d333

Nonce

2,612

Timestamp

8/7/2013, 5:56:17 AM

Confirmations

6,707,008

Mined by

⛏️ P2SHALTk1LjWrgsaAB9u4iJ7W2hf75g9mwE8Jj

Merkle Root

7a8bdbaf44a2c3db704ce97541bddd24969066621678799573f68da1109260b0

Transactions (1)

Coinbase7a8bdbaf44a2c3…f68da1109260b0

1 in → 1 out11.0600 XPM109 B

ALTk1LjW…g9mwE8Jj

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.

3.132 × 10¹¹⁶(117-digit number)

31322648554219593143…66318666444807080721

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

3.132 × 10¹¹⁶(117-digit number)

31322648554219593143…66318666444807080721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.264 × 10¹¹⁶(117-digit number)

62645297108439186286…32637332889614161441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.252 × 10¹¹⁷(118-digit number)

12529059421687837257…65274665779228322881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.505 × 10¹¹⁷(118-digit number)

25058118843375674514…30549331558456645761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.011 × 10¹¹⁷(118-digit number)

50116237686751349029…61098663116913291521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.002 × 10¹¹⁸(119-digit number)

10023247537350269805…22197326233826583041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.004 × 10¹¹⁸(119-digit number)

20046495074700539611…44394652467653166081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.009 × 10¹¹⁸(119-digit number)

40092990149401079223…88789304935306332161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.018 × 10¹¹⁸(119-digit number)

80185980298802158447…77578609870612664321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Block #102,693

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