Block #482,371

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/9/2014, 11:05:15 AM · Difficulty 10.5445 · 6,344,104 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6b89a6fb502d9feb8fd51e67da3df43b2857afe2cff8e0e6160db5dcd43dbbd0

Height

#482,371

Difficulty

10.544480

Transactions

4

Size

995 B

Version

2

Bits

0a8b6309

Nonce

31,108

Timestamp

4/9/2014, 11:05:15 AM

Confirmations

6,344,104

Merkle Root

5e2b6f4aac044e79670ab696b02c702f34ac1210c5f7bda06238dec77fcc16a6
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.

2.426 × 10¹⁰²(103-digit number)
24268881914687755620…25463776793089935361
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
2.426 × 10¹⁰²(103-digit number)
24268881914687755620…25463776793089935361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.853 × 10¹⁰²(103-digit number)
48537763829375511241…50927553586179870721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.707 × 10¹⁰²(103-digit number)
97075527658751022482…01855107172359741441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.941 × 10¹⁰³(104-digit number)
19415105531750204496…03710214344719482881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.883 × 10¹⁰³(104-digit number)
38830211063500408993…07420428689438965761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.766 × 10¹⁰³(104-digit number)
77660422127000817986…14840857378877931521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.553 × 10¹⁰⁴(105-digit number)
15532084425400163597…29681714757755863041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.106 × 10¹⁰⁴(105-digit number)
31064168850800327194…59363429515511726081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.212 × 10¹⁰⁴(105-digit number)
62128337701600654388…18726859031023452161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.242 × 10¹⁰⁵(106-digit number)
12425667540320130877…37453718062046904321
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:57,855,938 XPM·at block #6,826,474 · updates every 60s
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