Block #482,176

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/9/2014, 8:27:31 AM · Difficulty 10.5409 · 6,330,302 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
149ce1b68b72b52ae46544a95fde97df0159273a7f8bb93dc21bcfd922f9b118

Height

#482,176

Difficulty

10.540927

Transactions

1

Size

901 B

Version

2

Bits

0a8a7a31

Nonce

4,158

Timestamp

4/9/2014, 8:27:31 AM

Confirmations

6,330,302

Merkle Root

2469f1863f10d32fcdb2fc1d72d85e8729d7b607412f8d57cee5dcd14e62033e
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.

5.580 × 10⁹⁷(98-digit number)
55805109272506050485…33882322806726266881
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
5.580 × 10⁹⁷(98-digit number)
55805109272506050485…33882322806726266881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.116 × 10⁹⁸(99-digit number)
11161021854501210097…67764645613452533761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.232 × 10⁹⁸(99-digit number)
22322043709002420194…35529291226905067521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.464 × 10⁹⁸(99-digit number)
44644087418004840388…71058582453810135041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.928 × 10⁹⁸(99-digit number)
89288174836009680777…42117164907620270081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.785 × 10⁹⁹(100-digit number)
17857634967201936155…84234329815240540161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.571 × 10⁹⁹(100-digit number)
35715269934403872311…68468659630481080321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.143 × 10⁹⁹(100-digit number)
71430539868807744622…36937319260962160641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.428 × 10¹⁰⁰(101-digit number)
14286107973761548924…73874638521924321281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.857 × 10¹⁰⁰(101-digit number)
28572215947523097848…47749277043848642561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.714 × 10¹⁰⁰(101-digit number)
57144431895046195697…95498554087697285121
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,743,852 XPM·at block #6,812,477 · updates every 60s
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