Block #235,032

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/30/2013, 4:39:35 PM · Difficulty 9.9449 · 6,570,175 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2878169d43e7075c7db9486b4f2375c6e2004a96c6a3f3f46022b8c974495a9f

View on Chainz ↗

Height

#235,032

Difficulty

9.944937

Transactions

Size

1.75 KB

Version

Bits

09f1e75d

Nonce

1,170

Timestamp

10/30/2013, 4:39:35 PM

Confirmations

6,570,175

Mined by

⛏️ Rq5ALFWpHxdgP5jRvrZYxZVvW8nMMzhX7LjhL

Merkle Root

a55eb176438e0faa9602dccfc0773634fa996e0f926826b181d8e3a26007aafd

Transactions (1)

Coinbasea55eb176438e0f…d8e3a26007aafd

1 in → 48 out10.0800 XPM1.65 KB

ALFWpHxd…zhX7LjhL AFqKfjez…qX9Ace3g AMypZdXS…5jJKu8wP APVGazMT…cDCk2nwA ANuKx9Ke…wm7nrBRq

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.

1.837 × 10¹⁰²(103-digit number)

18370382130449376245…40487252301790576641

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

1.837 × 10¹⁰²(103-digit number)

18370382130449376245…40487252301790576641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.674 × 10¹⁰²(103-digit number)

36740764260898752491…80974504603581153281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.348 × 10¹⁰²(103-digit number)

73481528521797504983…61949009207162306561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.469 × 10¹⁰³(104-digit number)

14696305704359500996…23898018414324613121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.939 × 10¹⁰³(104-digit number)

29392611408719001993…47796036828649226241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.878 × 10¹⁰³(104-digit number)

58785222817438003986…95592073657298452481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.175 × 10¹⁰⁴(105-digit number)

11757044563487600797…91184147314596904961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.351 × 10¹⁰⁴(105-digit number)

23514089126975201594…82368294629193809921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.702 × 10¹⁰⁴(105-digit number)

47028178253950403189…64736589258387619841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.405 × 10¹⁰⁴(105-digit number)

94056356507900806379…29473178516775239681

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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