Block #368,483

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/20/2014, 6:23:34 PM · Difficulty 10.4427 · 6,439,882 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9b178eae5157faa79699b8fda1cb249ae756ed738ffc5635bf68b43bea5b0424

Height

#368,483

Difficulty

10.442703

Transactions

1

Size

968 B

Version

2

Bits

0a7154f6

Nonce

76,441

Timestamp

1/20/2014, 6:23:34 PM

Confirmations

6,439,882

Merkle Root

11c802af3c78f8c7c150c11c6848a6d42ed5f77db852f2a9ad380c3cafc5b8f9
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.

7.152 × 10⁹³(94-digit number)
71520362519587730076…95254034950067891681
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
7.152 × 10⁹³(94-digit number)
71520362519587730076…95254034950067891681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.430 × 10⁹⁴(95-digit number)
14304072503917546015…90508069900135783361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.860 × 10⁹⁴(95-digit number)
28608145007835092030…81016139800271566721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.721 × 10⁹⁴(95-digit number)
57216290015670184061…62032279600543133441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.144 × 10⁹⁵(96-digit number)
11443258003134036812…24064559201086266881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.288 × 10⁹⁵(96-digit number)
22886516006268073624…48129118402172533761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.577 × 10⁹⁵(96-digit number)
45773032012536147249…96258236804345067521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.154 × 10⁹⁵(96-digit number)
91546064025072294498…92516473608690135041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.830 × 10⁹⁶(97-digit number)
18309212805014458899…85032947217380270081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.661 × 10⁹⁶(97-digit number)
36618425610028917799…70065894434760540161
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:57,710,973 XPM·at block #6,808,364 · updates every 60s
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