Block #87,239

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 6:10:18 PM · Difficulty 9.2776 · 6,702,701 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

05c3bb6ae3f838641e11e7fa44d8ace877a8a9b82e4b7821a674094c6ecac079

View on Chainz ↗

Height

#87,239

Difficulty

9.277638

Transactions

Size

738 B

Version

Bits

0947134d

Nonce

8,700

Timestamp

7/28/2013, 6:10:18 PM

Confirmations

6,702,701

Merkle Root

0bafcce9a5c67758b90d1894654cfc5194a81398a0a9cf168960e94c506e8f4b

Transactions (3)

Coinbase069ef6c602f75c…0eaffdf38a263e

1 in → 1 out11.6227 XPM109 B

AeQsdAhA…EYtVaoF4

413c53a3239de4…8b226c09f055c3

2 in → 1 out2.3440 XPM341 B

AWeUvpc9…LLdip7UC

fe6889fe579aad…e9e68bfcf50ffa

1 in → 1 out23.2700 XPM192 B

AU1zg29c…USyMLb9b

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.

6.942 × 10¹⁰⁸(109-digit number)

69428716059556450461…28101784214509839039

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

6.942 × 10¹⁰⁸(109-digit number)

69428716059556450461…28101784214509839039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.388 × 10¹⁰⁹(110-digit number)

13885743211911290092…56203568429019678079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.777 × 10¹⁰⁹(110-digit number)

27771486423822580184…12407136858039356159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.554 × 10¹⁰⁹(110-digit number)

55542972847645160369…24814273716078712319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.110 × 10¹¹⁰(111-digit number)

11108594569529032073…49628547432157424639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.221 × 10¹¹⁰(111-digit number)

22217189139058064147…99257094864314849279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.443 × 10¹¹⁰(111-digit number)

44434378278116128295…98514189728629698559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.886 × 10¹¹⁰(111-digit number)

88868756556232256590…97028379457259397119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.777 × 10¹¹¹(112-digit number)

17773751311246451318…94056758914518794239

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