Block #239,242

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2013, 11:49:16 PM · Difficulty 9.9541 · 6,575,861 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
929f5a45c7c2be80000c9c3ace4176c7f75aed5c2e705c65397319b465ca53af

Height

#239,242

Difficulty

9.954081

Transactions

3

Size

53.99 KB

Version

2

Bits

09f43ea2

Nonce

13,328

Timestamp

11/1/2013, 11:49:16 PM

Confirmations

6,575,861

Merkle Root

809092ee435d4911339f754ae74be08752125eba309193c63fdb14b0a8171f27
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.

9.653 × 10⁹⁷(98-digit number)
96537040411063067374…55998697411439168801
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.

1
origin + 1
9.653 × 10⁹⁷(98-digit number)
96537040411063067374…55998697411439168801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.930 × 10⁹⁸(99-digit number)
19307408082212613474…11997394822878337601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.861 × 10⁹⁸(99-digit number)
38614816164425226949…23994789645756675201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.722 × 10⁹⁸(99-digit number)
77229632328850453899…47989579291513350401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.544 × 10⁹⁹(100-digit number)
15445926465770090779…95979158583026700801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.089 × 10⁹⁹(100-digit number)
30891852931540181559…91958317166053401601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.178 × 10⁹⁹(100-digit number)
61783705863080363119…83916634332106803201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.235 × 10¹⁰⁰(101-digit number)
12356741172616072623…67833268664213606401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.471 × 10¹⁰⁰(101-digit number)
24713482345232145247…35666537328427212801
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, …
Circulating Supply:57,764,913 XPM·at block #6,815,102 · updates every 60s
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