Block #94,874

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 8:59:21 AM · Difficulty 9.2100 · 6,721,947 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cf0ae911ced00fca0554fe34224f070af430d7b5ef7ec285e211fa5930bf61c5

View on Chainz ↗

Height

#94,874

Difficulty

9.209971

Transactions

Size

481 B

Version

Bits

0935c0a6

Nonce

93,430

Timestamp

8/3/2013, 8:59:21 AM

Confirmations

6,721,947

Mined by

⛏️ P2SHAcF4Z7rikJ9Rgm91NAfPp7wTVio4HzLwKu

Merkle Root

ac9004993f255f05df207351bdff57e9335fa437e3ebe2d437a36aab4802b6a5

Transactions (2)

Coinbasea5b9efcdb6c17f…bab3a1e83b2bf9

1 in → 1 out11.7800 XPM109 B

AcF4Z7ri…o4HzLwKu

1a2e704aca64d3…ec65366580e033

2 in → 1 out23.8400 XPM273 B

AcS31cBK…Dmi7rdMj

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.

1.061 × 10¹¹⁷(118-digit number)

10618094566892706229…30165610127600262399

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

1.061 × 10¹¹⁷(118-digit number)

10618094566892706229…30165610127600262399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.123 × 10¹¹⁷(118-digit number)

21236189133785412459…60331220255200524799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.247 × 10¹¹⁷(118-digit number)

42472378267570824919…20662440510401049599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.494 × 10¹¹⁷(118-digit number)

84944756535141649838…41324881020802099199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.698 × 10¹¹⁸(119-digit number)

16988951307028329967…82649762041604198399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.397 × 10¹¹⁸(119-digit number)

33977902614056659935…65299524083208396799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.795 × 10¹¹⁸(119-digit number)

67955805228113319870…30599048166416793599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.359 × 10¹¹⁹(120-digit number)

13591161045622663974…61198096332833587199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.718 × 10¹¹⁹(120-digit number)

27182322091245327948…22396192665667174399

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 #94,874

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