Block #237,360

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2013, 12:17:14 AM · Difficulty 9.9495 · 6,577,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2e1e8c41aa37f9cf27616c61c8267e8f2258f22a0a14a90e17aeba52548f8dd3

Height

#237,360

Difficulty

9.949541

Transactions

3

Size

803 B

Version

2

Bits

09f3151d

Nonce

3,922

Timestamp

11/1/2013, 12:17:14 AM

Confirmations

6,577,738

Merkle Root

aaa1ade116fd0bc3c6278e53d736dce196edbf646d285346329966a554618f3e
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.

3.769 × 10⁹⁷(98-digit number)
37697286846261405983…28260077247891068801
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
3.769 × 10⁹⁷(98-digit number)
37697286846261405983…28260077247891068801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.539 × 10⁹⁷(98-digit number)
75394573692522811966…56520154495782137601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.507 × 10⁹⁸(99-digit number)
15078914738504562393…13040308991564275201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.015 × 10⁹⁸(99-digit number)
30157829477009124786…26080617983128550401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.031 × 10⁹⁸(99-digit number)
60315658954018249573…52161235966257100801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.206 × 10⁹⁹(100-digit number)
12063131790803649914…04322471932514201601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.412 × 10⁹⁹(100-digit number)
24126263581607299829…08644943865028403201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.825 × 10⁹⁹(100-digit number)
48252527163214599658…17289887730056806401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.650 × 10⁹⁹(100-digit number)
96505054326429199317…34579775460113612801
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,764,873 XPM·at block #6,815,097 · updates every 60s
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