Block #371,172

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2014, 4:15:04 PM · Difficulty 10.4364 · 6,425,005 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
71bcf6b4536db8565d86b90c03ea976723c71bda0bc76aa9b80e9ddcf5d85e89

Height

#371,172

Difficulty

10.436443

Transactions

3

Size

653 B

Version

2

Bits

0a6fbaba

Nonce

140,267

Timestamp

1/22/2014, 4:15:04 PM

Confirmations

6,425,005

Merkle Root

2e17e4ccfbb24bea071ed4f206858233090e6d1ae35d39f8a631fe8d0331015d
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.

1.370 × 10⁹⁸(99-digit number)
13705242068310840392…92028466959597634701
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
1.370 × 10⁹⁸(99-digit number)
13705242068310840392…92028466959597634701
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.741 × 10⁹⁸(99-digit number)
27410484136621680784…84056933919195269401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.482 × 10⁹⁸(99-digit number)
54820968273243361568…68113867838390538801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.096 × 10⁹⁹(100-digit number)
10964193654648672313…36227735676781077601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.192 × 10⁹⁹(100-digit number)
21928387309297344627…72455471353562155201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.385 × 10⁹⁹(100-digit number)
43856774618594689254…44910942707124310401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.771 × 10⁹⁹(100-digit number)
87713549237189378509…89821885414248620801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.754 × 10¹⁰⁰(101-digit number)
17542709847437875701…79643770828497241601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.508 × 10¹⁰⁰(101-digit number)
35085419694875751403…59287541656994483201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.017 × 10¹⁰⁰(101-digit number)
70170839389751502807…18575083313988966401
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:57,613,415 XPM·at block #6,796,176 · updates every 60s
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