Block #484,625

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 3:28:57 PM · Difficulty 10.5921 · 6,322,541 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cc9588043abf225fd1fe7e06d53fb67f638061f91fd94e3952ea71468a910e9

Height

#484,625

Difficulty

10.592082

Transactions

3

Size

810 B

Version

2

Bits

0a9792ab

Nonce

253,067,454

Timestamp

4/10/2014, 3:28:57 PM

Confirmations

6,322,541

Merkle Root

6374016086ff1111435e3fd9527f064f9964a2b1e36c9ce1519ec5c5853ac439
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.

2.290 × 10⁹⁸(99-digit number)
22905180814254804289…21713354192747592001
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
2.290 × 10⁹⁸(99-digit number)
22905180814254804289…21713354192747592001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.581 × 10⁹⁸(99-digit number)
45810361628509608578…43426708385495184001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.162 × 10⁹⁸(99-digit number)
91620723257019217156…86853416770990368001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.832 × 10⁹⁹(100-digit number)
18324144651403843431…73706833541980736001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.664 × 10⁹⁹(100-digit number)
36648289302807686862…47413667083961472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.329 × 10⁹⁹(100-digit number)
73296578605615373724…94827334167922944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.465 × 10¹⁰⁰(101-digit number)
14659315721123074744…89654668335845888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.931 × 10¹⁰⁰(101-digit number)
29318631442246149489…79309336671691776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.863 × 10¹⁰⁰(101-digit number)
58637262884492298979…58618673343383552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.172 × 10¹⁰¹(102-digit number)
11727452576898459795…17237346686767104001
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:57,701,337 XPM·at block #6,807,165 · updates every 60s
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