Block #375,647

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 8:45:46 PM · Difficulty 10.4245 · 6,434,831 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
910623459f17e20228c31507166738630c1ed57ca359344dbbcf305ccd1f44b2

Height

#375,647

Difficulty

10.424545

Transactions

2

Size

1.23 KB

Version

2

Bits

0a6caf02

Nonce

23,567

Timestamp

1/25/2014, 8:45:46 PM

Confirmations

6,434,831

Merkle Root

892f5a1535c0e9087c322b3e8c704a1637018bba03f4add14caa7eb76430e1d2
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.

2.266 × 10⁹⁷(98-digit number)
22663743481000632736…46597714126343103561
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
2.266 × 10⁹⁷(98-digit number)
22663743481000632736…46597714126343103561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.532 × 10⁹⁷(98-digit number)
45327486962001265472…93195428252686207121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.065 × 10⁹⁷(98-digit number)
90654973924002530944…86390856505372414241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.813 × 10⁹⁸(99-digit number)
18130994784800506188…72781713010744828481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.626 × 10⁹⁸(99-digit number)
36261989569601012377…45563426021489656961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.252 × 10⁹⁸(99-digit number)
72523979139202024755…91126852042979313921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.450 × 10⁹⁹(100-digit number)
14504795827840404951…82253704085958627841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.900 × 10⁹⁹(100-digit number)
29009591655680809902…64507408171917255681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.801 × 10⁹⁹(100-digit number)
58019183311361619804…29014816343834511361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.160 × 10¹⁰⁰(101-digit number)
11603836662272323960…58029632687669022721
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:57,727,903 XPM·at block #6,810,477 · updates every 60s
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