Block #377,324

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 12:55:08 AM · Difficulty 10.4234 · 6,432,136 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bb9bb2f62b63cce4d08045bf31b3b14da84a6d370461d75dbd4c8e5a2cf209e

Height

#377,324

Difficulty

10.423432

Transactions

5

Size

3.69 KB

Version

2

Bits

0a6c6610

Nonce

131,636

Timestamp

1/27/2014, 12:55:08 AM

Confirmations

6,432,136

Merkle Root

10463ad00e33f70db5f0516a32fe539f7793285f4c6c1251f21b8d70bdc4b8d7
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.

1.089 × 10¹⁰⁶(107-digit number)
10891314218654022112…35065704947135183041
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
1.089 × 10¹⁰⁶(107-digit number)
10891314218654022112…35065704947135183041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.178 × 10¹⁰⁶(107-digit number)
21782628437308044224…70131409894270366081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.356 × 10¹⁰⁶(107-digit number)
43565256874616088448…40262819788540732161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.713 × 10¹⁰⁶(107-digit number)
87130513749232176896…80525639577081464321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.742 × 10¹⁰⁷(108-digit number)
17426102749846435379…61051279154162928641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.485 × 10¹⁰⁷(108-digit number)
34852205499692870758…22102558308325857281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.970 × 10¹⁰⁷(108-digit number)
69704410999385741517…44205116616651714561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.394 × 10¹⁰⁸(109-digit number)
13940882199877148303…88410233233303429121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.788 × 10¹⁰⁸(109-digit number)
27881764399754296606…76820466466606858241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.576 × 10¹⁰⁸(109-digit number)
55763528799508593213…53640932933213716481
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, …
Circulating Supply:57,719,752 XPM·at block #6,809,459 · updates every 60s
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