Block #69,705

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 10:04:37 AM · Difficulty 8.9913 · 6,724,933 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c42c3a69e49c948952285cb13abf7c8aec016caca7d4b365fc93d5a9de0955e0

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Height

#69,705

Difficulty

8.991272

Transactions

Size

203 B

Version

Bits

08fdc407

Nonce

481

Timestamp

7/20/2013, 10:04:37 AM

Confirmations

6,724,933

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

4d9c9325e344e431748728db018b4112b06e0531a48eda1aa8e22d1b74226e08

Transactions (1)

Coinbase4d9c9325e344e4…e22d1b74226e08

1 in → 1 out12.3500 XPM110 B

AXSFye4r…ADf1YWCU

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.

3.384 × 10¹⁰¹(102-digit number)

33848106191024840207…30366072348450771199

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

3.384 × 10¹⁰¹(102-digit number)

33848106191024840207…30366072348450771199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.769 × 10¹⁰¹(102-digit number)

67696212382049680414…60732144696901542399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.353 × 10¹⁰²(103-digit number)

13539242476409936082…21464289393803084799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.707 × 10¹⁰²(103-digit number)

27078484952819872165…42928578787606169599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.415 × 10¹⁰²(103-digit number)

54156969905639744331…85857157575212339199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.083 × 10¹⁰³(104-digit number)

10831393981127948866…71714315150424678399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.166 × 10¹⁰³(104-digit number)

21662787962255897732…43428630300849356799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.332 × 10¹⁰³(104-digit number)

43325575924511795465…86857260601698713599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

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 1CC formula:

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

Cross-reference on Chainz Explorer