Block #492,628

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2014, 6:35:29 AM · Difficulty 10.6883 · 6,323,337 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0307afc02f59d801b5cfc93a5dc52bb5cf61843a72a86178419d1966a5ae1121

Height

#492,628

Difficulty

10.688322

Transactions

3

Size

658 B

Version

2

Bits

0ab035e2

Nonce

87,583,784

Timestamp

4/15/2014, 6:35:29 AM

Confirmations

6,323,337

Merkle Root

d795ce88b0f12bbd732e94767eb43f1005685a4c67bd958892ce1fc81c65194e
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.

6.282 × 10⁹⁹(100-digit number)
62829218387052972853…99408248835258859521
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
6.282 × 10⁹⁹(100-digit number)
62829218387052972853…99408248835258859521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.256 × 10¹⁰⁰(101-digit number)
12565843677410594570…98816497670517719041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.513 × 10¹⁰⁰(101-digit number)
25131687354821189141…97632995341035438081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.026 × 10¹⁰⁰(101-digit number)
50263374709642378282…95265990682070876161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.005 × 10¹⁰¹(102-digit number)
10052674941928475656…90531981364141752321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.010 × 10¹⁰¹(102-digit number)
20105349883856951313…81063962728283504641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.021 × 10¹⁰¹(102-digit number)
40210699767713902626…62127925456567009281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.042 × 10¹⁰¹(102-digit number)
80421399535427805252…24255850913134018561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.608 × 10¹⁰²(103-digit number)
16084279907085561050…48511701826268037121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.216 × 10¹⁰²(103-digit number)
32168559814171122100…97023403652536074241
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:57,771,831 XPM·at block #6,815,964 · updates every 60s
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