Block #94,339

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 12:56:56 AM · Difficulty 9.2021 · 6,713,112 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cf1378c867f99d69ce76a3ad3317e7f292256e12a24ab6281ec878d7eb072697

View on Chainz ↗

Height

#94,339

Difficulty

9.202112

Transactions

Size

207 B

Version

Bits

0933bd98

Nonce

817,989

Timestamp

8/3/2013, 12:56:56 AM

Confirmations

6,713,112

Mined by

⛏️ P2SHAJwT4t7mqNZ7nwyuBKJTxL3n2nrXZrFS9k

Merkle Root

629c79c5a45dc97401f1da5092740b2ad06d18cdbb45307bb6c1cb9921d99c69

Transactions (1)

Coinbase629c79c5a45dc9…c1cb9921d99c69

1 in → 1 out11.7900 XPM109 B

AJwT4t7m…rXZrFS9k

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.

3.969 × 10¹¹⁴(115-digit number)

39694911147581539990…00413181960583398399

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

3.969 × 10¹¹⁴(115-digit number)

39694911147581539990…00413181960583398399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.938 × 10¹¹⁴(115-digit number)

79389822295163079981…00826363921166796799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.587 × 10¹¹⁵(116-digit number)

15877964459032615996…01652727842333593599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.175 × 10¹¹⁵(116-digit number)

31755928918065231992…03305455684667187199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.351 × 10¹¹⁵(116-digit number)

63511857836130463984…06610911369334374399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.270 × 10¹¹⁶(117-digit number)

12702371567226092796…13221822738668748799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.540 × 10¹¹⁶(117-digit number)

25404743134452185593…26443645477337497599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.080 × 10¹¹⁶(117-digit number)

50809486268904371187…52887290954674995199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.016 × 10¹¹⁷(118-digit number)

10161897253780874237…05774581909349990399

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 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 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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #94,339

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