Block #87,602

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 12:52:41 AM · Difficulty 9.2718 · 6,703,341 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1f18430b7310fba9b39764eac81ebc1b660760ca7b8ed2d81c5faf925005bd1e

View on Chainz ↗

Height

#87,602

Difficulty

9.271752

Transactions

Size

201 B

Version

Bits

09459183

Nonce

38,648

Timestamp

7/29/2013, 12:52:41 AM

Confirmations

6,703,341

Merkle Root

6a6eb3756be2e96846170567a8193c97afdb40576be427ef53012449408d2e69

Transactions (1)

Coinbase6a6eb3756be2e9…012449408d2e69

1 in → 1 out11.6200 XPM109 B

AcuJraLT…Y66BS47Q

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.

1.790 × 10¹⁰⁰(101-digit number)

17905267951837034312…51107407083698285121

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

1.790 × 10¹⁰⁰(101-digit number)

17905267951837034312…51107407083698285121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.581 × 10¹⁰⁰(101-digit number)

35810535903674068625…02214814167396570241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.162 × 10¹⁰⁰(101-digit number)

71621071807348137251…04429628334793140481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.432 × 10¹⁰¹(102-digit number)

14324214361469627450…08859256669586280961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.864 × 10¹⁰¹(102-digit number)

28648428722939254900…17718513339172561921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.729 × 10¹⁰¹(102-digit number)

57296857445878509801…35437026678345123841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.145 × 10¹⁰²(103-digit number)

11459371489175701960…70874053356690247681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.291 × 10¹⁰²(103-digit number)

22918742978351403920…41748106713380495361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.583 × 10¹⁰²(103-digit number)

45837485956702807841…83496213426760990721

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer