Block #376,314

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/26/2014, 8:09:35 AM · Difficulty 10.4228 · 6,432,849 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
26417d4c5c3b2a324bed4bb3017a4bc181c7c0538a296bfc73149e5c1af09e5d

Height

#376,314

Difficulty

10.422835

Transactions

3

Size

914 B

Version

2

Bits

0a6c3ef0

Nonce

75,079

Timestamp

1/26/2014, 8:09:35 AM

Confirmations

6,432,849

Merkle Root

93e120132b0f38e0ead235d1781b290e4de0b7615473b4bcbd9e9fa024916b60
Transactions (3)
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.

7.911 × 10⁹⁸(99-digit number)
79114290992534541298…50881168534008627121
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
7.911 × 10⁹⁸(99-digit number)
79114290992534541298…50881168534008627121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.582 × 10⁹⁹(100-digit number)
15822858198506908259…01762337068017254241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.164 × 10⁹⁹(100-digit number)
31645716397013816519…03524674136034508481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.329 × 10⁹⁹(100-digit number)
63291432794027633038…07049348272069016961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.265 × 10¹⁰⁰(101-digit number)
12658286558805526607…14098696544138033921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.531 × 10¹⁰⁰(101-digit number)
25316573117611053215…28197393088276067841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.063 × 10¹⁰⁰(101-digit number)
50633146235222106430…56394786176552135681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.012 × 10¹⁰¹(102-digit number)
10126629247044421286…12789572353104271361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.025 × 10¹⁰¹(102-digit number)
20253258494088842572…25579144706208542721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.050 × 10¹⁰¹(102-digit number)
40506516988177685144…51158289412417085441
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:57,717,365 XPM·at block #6,809,162 · updates every 60s
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