Block #374,127

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 7:06:51 PM · Difficulty 10.4264 · 6,435,441 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
44257008d9a4dc8eb9e98c26aa5fcf49a9b5b2cfdecf1afbcb1649aaac65046d

Height

#374,127

Difficulty

10.426396

Transactions

3

Size

946 B

Version

2

Bits

0a6d284b

Nonce

127,320

Timestamp

1/24/2014, 7:06:51 PM

Confirmations

6,435,441

Merkle Root

302d809fa332ba87bdf89d598044b891448aa0f396060105ba6c901c4bc4c2a0
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.

4.113 × 10⁹⁰(91-digit number)
41134545752149937665…77088027650793250641
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
4.113 × 10⁹⁰(91-digit number)
41134545752149937665…77088027650793250641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.226 × 10⁹⁰(91-digit number)
82269091504299875331…54176055301586501281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.645 × 10⁹¹(92-digit number)
16453818300859975066…08352110603173002561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.290 × 10⁹¹(92-digit number)
32907636601719950132…16704221206346005121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.581 × 10⁹¹(92-digit number)
65815273203439900265…33408442412692010241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.316 × 10⁹²(93-digit number)
13163054640687980053…66816884825384020481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.632 × 10⁹²(93-digit number)
26326109281375960106…33633769650768040961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.265 × 10⁹²(93-digit number)
52652218562751920212…67267539301536081921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.053 × 10⁹³(94-digit number)
10530443712550384042…34535078603072163841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.106 × 10⁹³(94-digit number)
21060887425100768084…69070157206144327681
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:57,720,620 XPM·at block #6,809,567 · updates every 60s
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