Block #366,000

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/19/2014, 3:29:50 AM · Difficulty 10.4256 · 6,439,695 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94618578e15428876972926b41883d9ea1fb9da598a5131777eb8e2b01e1d5e2

Height

#366,000

Difficulty

10.425558

Transactions

4

Size

3.67 KB

Version

2

Bits

0a6cf15a

Nonce

27,514

Timestamp

1/19/2014, 3:29:50 AM

Confirmations

6,439,695

Merkle Root

4eab390dc00058d82995c3d820786202a5a085e2da8fbb398daf018cb3d262c0
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.

4.498 × 10⁸⁸(89-digit number)
44982119350192704445…54762920929492610071
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
4.498 × 10⁸⁸(89-digit number)
44982119350192704445…54762920929492610071
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.996 × 10⁸⁸(89-digit number)
89964238700385408891…09525841858985220141
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.799 × 10⁸⁹(90-digit number)
17992847740077081778…19051683717970440281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.598 × 10⁸⁹(90-digit number)
35985695480154163556…38103367435940880561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.197 × 10⁸⁹(90-digit number)
71971390960308327113…76206734871881761121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.439 × 10⁹⁰(91-digit number)
14394278192061665422…52413469743763522241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.878 × 10⁹⁰(91-digit number)
28788556384123330845…04826939487527044481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.757 × 10⁹⁰(91-digit number)
57577112768246661690…09653878975054088961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.151 × 10⁹¹(92-digit number)
11515422553649332338…19307757950108177921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.303 × 10⁹¹(92-digit number)
23030845107298664676…38615515900216355841
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:57,689,641 XPM·at block #6,805,694 · updates every 60s
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