Block #956,681

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/1/2015, 5:27:18 AM · Difficulty 10.8904 · 5,870,280 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c04a9b6ab3547196944ba067dfb2a58f4c1da20653f8d8c89c2e5e1c1f5a6a1d

Height

#956,681

Difficulty

10.890398

Transactions

2

Size

2.02 KB

Version

2

Bits

0ae3f11a

Nonce

127,410,057

Timestamp

3/1/2015, 5:27:18 AM

Confirmations

5,870,280

Merkle Root

cec516bd0ee7b483b920381fa795594f61637cd7ad372f61cb5a2cb18ef5b86e
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.

1.149 × 10⁹⁶(97-digit number)
11494833889304911830…47790650261145409801
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
1.149 × 10⁹⁶(97-digit number)
11494833889304911830…47790650261145409801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.298 × 10⁹⁶(97-digit number)
22989667778609823661…95581300522290819601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.597 × 10⁹⁶(97-digit number)
45979335557219647322…91162601044581639201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.195 × 10⁹⁶(97-digit number)
91958671114439294644…82325202089163278401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.839 × 10⁹⁷(98-digit number)
18391734222887858928…64650404178326556801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.678 × 10⁹⁷(98-digit number)
36783468445775717857…29300808356653113601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.356 × 10⁹⁷(98-digit number)
73566936891551435715…58601616713306227201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.471 × 10⁹⁸(99-digit number)
14713387378310287143…17203233426612454401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.942 × 10⁹⁸(99-digit number)
29426774756620574286…34406466853224908801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.885 × 10⁹⁸(99-digit number)
58853549513241148572…68812933706449817601
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:57,859,864 XPM·at block #6,826,960 · updates every 60s
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