Block #1,182,043

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/4/2015, 12:16:17 AM · Difficulty 10.9158 · 5,626,019 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc0991f45ba3d19d025a66e5aa20b7ba61e18d05e5c80262f74b99fae537b588

Height

#1,182,043

Difficulty

10.915833

Transactions

2

Size

424 B

Version

2

Bits

0aea740a

Nonce

234,094,863

Timestamp

8/4/2015, 12:16:17 AM

Confirmations

5,626,019

Merkle Root

feec10fbed17387e183a0e6c256955ad545a6a71c4109319454d5ad89994fff0
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.

8.594 × 10⁹⁴(95-digit number)
85944324700343757212…41154152315143640321
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
8.594 × 10⁹⁴(95-digit number)
85944324700343757212…41154152315143640321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.718 × 10⁹⁵(96-digit number)
17188864940068751442…82308304630287280641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.437 × 10⁹⁵(96-digit number)
34377729880137502885…64616609260574561281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.875 × 10⁹⁵(96-digit number)
68755459760275005770…29233218521149122561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.375 × 10⁹⁶(97-digit number)
13751091952055001154…58466437042298245121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.750 × 10⁹⁶(97-digit number)
27502183904110002308…16932874084596490241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.500 × 10⁹⁶(97-digit number)
55004367808220004616…33865748169192980481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.100 × 10⁹⁷(98-digit number)
11000873561644000923…67731496338385960961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.200 × 10⁹⁷(98-digit number)
22001747123288001846…35462992676771921921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.400 × 10⁹⁷(98-digit number)
44003494246576003692…70925985353543843841
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:57,708,540 XPM·at block #6,808,061 · updates every 60s
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