Block #482,237

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/9/2014, 9:23:39 AM · Difficulty 10.5415 · 6,320,817 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94fe5941156c9c5af5ee9dfd5fb0c82b7966762bed7eb6a5389a643995a68fad

Height

#482,237

Difficulty

10.541499

Transactions

4

Size

1.01 KB

Version

2

Bits

0a8a9fb5

Nonce

21,759,643

Timestamp

4/9/2014, 9:23:39 AM

Confirmations

6,320,817

Merkle Root

861441921342d7c6bf14844e67826aeb043b87f0e80f41ea9a529bfd17a7e891
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.

1.000 × 10⁹⁹(100-digit number)
10002646279099590908…87063301641161531521
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
1.000 × 10⁹⁹(100-digit number)
10002646279099590908…87063301641161531521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.000 × 10⁹⁹(100-digit number)
20005292558199181816…74126603282323063041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.001 × 10⁹⁹(100-digit number)
40010585116398363632…48253206564646126081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.002 × 10⁹⁹(100-digit number)
80021170232796727264…96506413129292252161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.600 × 10¹⁰⁰(101-digit number)
16004234046559345452…93012826258584504321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.200 × 10¹⁰⁰(101-digit number)
32008468093118690905…86025652517169008641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.401 × 10¹⁰⁰(101-digit number)
64016936186237381811…72051305034338017281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.280 × 10¹⁰¹(102-digit number)
12803387237247476362…44102610068676034561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.560 × 10¹⁰¹(102-digit number)
25606774474494952724…88205220137352069121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.121 × 10¹⁰¹(102-digit number)
51213548948989905449…76410440274704138241
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:57,668,459 XPM·at block #6,803,053 · updates every 60s
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