Block #11,344

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/11/2013, 6:18:14 AM · Difficulty 7.7148 · 6,778,057 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a8d4e9ffa0a522e459830a0cd94b20fb218a2be60adc1ce30e73df3e91fe4f8

Height

#11,344

Difficulty

7.714817

Transactions

1

Size

200 B

Version

2

Bits

07b6fe3b

Nonce

584

Timestamp

7/11/2013, 6:18:14 AM

Confirmations

6,778,057

Merkle Root

920a8c5dd5587fa921b518422fde8c08832041726bb618018670770f352c2a5b
Transactions (1)
1 in → 1 out16.7800 XPM109 B
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.

2.575 × 10⁹⁶(97-digit number)
25759476127145995153…00912539559857705601
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
2.575 × 10⁹⁶(97-digit number)
25759476127145995153…00912539559857705601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.151 × 10⁹⁶(97-digit number)
51518952254291990307…01825079119715411201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.030 × 10⁹⁷(98-digit number)
10303790450858398061…03650158239430822401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.060 × 10⁹⁷(98-digit number)
20607580901716796123…07300316478861644801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.121 × 10⁹⁷(98-digit number)
41215161803433592246…14600632957723289601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.243 × 10⁹⁷(98-digit number)
82430323606867184492…29201265915446579201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.648 × 10⁹⁸(99-digit number)
16486064721373436898…58402531830893158401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,559,159 XPM·at block #6,789,400 · updates every 60s