Block #87,019

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 1:50:47 PM · Difficulty 9.2832 · 6,722,276 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7ff2f0b800789114c30663b2948f67ef434cbd1af2574be854eb100fd59cdd6c

View on Chainz ↗

Height

#87,019

Difficulty

9.283184

Transactions

Size

590 B

Version

Bits

09487eba

Nonce

117,271

Timestamp

7/28/2013, 1:50:47 PM

Confirmations

6,722,276

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

f515deef285be12dfc8b1e81c350911ef96f3af5d2db73eca7e0924d914c6c37

Transactions (3)

Coinbasedd3c3da6cc3f14…9ef4986e29f5c3

1 in → 1 out11.6100 XPM109 B

ATzEHZ7a…2eAGweip

8ec26b7e8f3ce0…006721422344ca

1 in → 2 out11.6100 XPM192 B

AaMRUFMG…S11BNFrC AGv2Aac9…fS6qJfM6

060c53a3438da9…c0363c05bd2a61

1 in → 1 out5.8000 XPM192 B

AeguK5Ai…CLUqoF9q

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.

3.568 × 10¹¹⁰(111-digit number)

35682121969344747661…99540398937970199359

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

3.568 × 10¹¹⁰(111-digit number)

35682121969344747661…99540398937970199359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.136 × 10¹¹⁰(111-digit number)

71364243938689495322…99080797875940398719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.427 × 10¹¹¹(112-digit number)

14272848787737899064…98161595751880797439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.854 × 10¹¹¹(112-digit number)

28545697575475798128…96323191503761594879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.709 × 10¹¹¹(112-digit number)

57091395150951596257…92646383007523189759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.141 × 10¹¹²(113-digit number)

11418279030190319251…85292766015046379519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.283 × 10¹¹²(113-digit number)

22836558060380638503…70585532030092759039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.567 × 10¹¹²(113-digit number)

45673116120761277006…41171064060185518079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.134 × 10¹¹²(113-digit number)

91346232241522554012…82342128120371036159

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 #87,019

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