Block #360,696

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/15/2014, 2:44:43 PM · Difficulty 10.3972 · 6,434,990 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77547096708f5981dad4bceff4e02e58ac43f47eb051bcd7cfe8cda002d8848f

Height

#360,696

Difficulty

10.397243

Transactions

3

Size

653 B

Version

2

Bits

0a65b1c0

Nonce

25,103

Timestamp

1/15/2014, 2:44:43 PM

Confirmations

6,434,990

Merkle Root

ef551a89c7d715e8f46a16cf5dee0dc95439ddf97a563bc0dde7ac507ceb7659
Transactions (3)
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.

6.565 × 10⁹⁶(97-digit number)
65659937521435648342…02869187898251198241
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
6.565 × 10⁹⁶(97-digit number)
65659937521435648342…02869187898251198241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.313 × 10⁹⁷(98-digit number)
13131987504287129668…05738375796502396481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.626 × 10⁹⁷(98-digit number)
26263975008574259336…11476751593004792961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.252 × 10⁹⁷(98-digit number)
52527950017148518673…22953503186009585921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.050 × 10⁹⁸(99-digit number)
10505590003429703734…45907006372019171841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.101 × 10⁹⁸(99-digit number)
21011180006859407469…91814012744038343681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.202 × 10⁹⁸(99-digit number)
42022360013718814939…83628025488076687361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.404 × 10⁹⁸(99-digit number)
84044720027437629878…67256050976153374721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.680 × 10⁹⁹(100-digit number)
16808944005487525975…34512101952306749441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.361 × 10⁹⁹(100-digit number)
33617888010975051951…69024203904613498881
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:57,609,557 XPM·at block #6,795,685 · updates every 60s
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