Block #368,828

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/20/2014, 11:42:24 PM · Difficulty 10.4456 · 6,439,059 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
20618fb1ca64fb62c2928a3ced66549f8411e4d51e87f841ebc4b363ddf2391f

Height

#368,828

Difficulty

10.445634

Transactions

3

Size

651 B

Version

2

Bits

0a721511

Nonce

508,824

Timestamp

1/20/2014, 11:42:24 PM

Confirmations

6,439,059

Merkle Root

61d0e7781a096be7b3995c38f54446d7871a9b615287ecebbe9967e0529e5067
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.

3.380 × 10⁹²(93-digit number)
33802546750090656525…77478958814969631281
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
3.380 × 10⁹²(93-digit number)
33802546750090656525…77478958814969631281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.760 × 10⁹²(93-digit number)
67605093500181313050…54957917629939262561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.352 × 10⁹³(94-digit number)
13521018700036262610…09915835259878525121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.704 × 10⁹³(94-digit number)
27042037400072525220…19831670519757050241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.408 × 10⁹³(94-digit number)
54084074800145050440…39663341039514100481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.081 × 10⁹⁴(95-digit number)
10816814960029010088…79326682079028200961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.163 × 10⁹⁴(95-digit number)
21633629920058020176…58653364158056401921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.326 × 10⁹⁴(95-digit number)
43267259840116040352…17306728316112803841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.653 × 10⁹⁴(95-digit number)
86534519680232080704…34613456632225607681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.730 × 10⁹⁵(96-digit number)
17306903936046416140…69226913264451215361
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:57,707,131 XPM·at block #6,807,886 · updates every 60s
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