Block #372,391

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2014, 1:52:27 PM · Difficulty 10.4278 · 6,426,424 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9e6c1eca1ff0d5bcd07c3ef9fecc6a2d37f9a98007592e6ecb09f3fb47a52b3

Height

#372,391

Difficulty

10.427753

Transactions

2

Size

580 B

Version

2

Bits

0a6d8140

Nonce

364

Timestamp

1/23/2014, 1:52:27 PM

Confirmations

6,426,424

Merkle Root

0d7dcd656b46ab83906f0affbd20a1e8447c9245dbf4026758ed3af3b87ab32f
Transactions (2)
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.

7.294 × 10⁹⁷(98-digit number)
72941188430769339212…23051974749615687121
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
7.294 × 10⁹⁷(98-digit number)
72941188430769339212…23051974749615687121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.458 × 10⁹⁸(99-digit number)
14588237686153867842…46103949499231374241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.917 × 10⁹⁸(99-digit number)
29176475372307735684…92207898998462748481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.835 × 10⁹⁸(99-digit number)
58352950744615471369…84415797996925496961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.167 × 10⁹⁹(100-digit number)
11670590148923094273…68831595993850993921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.334 × 10⁹⁹(100-digit number)
23341180297846188547…37663191987701987841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.668 × 10⁹⁹(100-digit number)
46682360595692377095…75326383975403975681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.336 × 10⁹⁹(100-digit number)
93364721191384754191…50652767950807951361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.867 × 10¹⁰⁰(101-digit number)
18672944238276950838…01305535901615902721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.734 × 10¹⁰⁰(101-digit number)
37345888476553901676…02611071803231805441
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:57,634,548 XPM·at block #6,798,814 · updates every 60s
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