Block #1,105,441

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/15/2015, 12:24:14 AM · Difficulty 10.7825 · 5,703,429 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c3ac587b6140874c161559293a38f002e0770dd1c483bfd472e254a0ec5ea742

Height

#1,105,441

Difficulty

10.782458

Transactions

2

Size

872 B

Version

2

Bits

0ac84f2f

Nonce

847,378,864

Timestamp

6/15/2015, 12:24:14 AM

Confirmations

5,703,429

Merkle Root

552a7ea57e3cd19bbd670866566d646607fe197e3ca92c7e96d4dab0e884812b
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.

8.486 × 10⁹⁶(97-digit number)
84865735336757169666…68885087557301196801
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
8.486 × 10⁹⁶(97-digit number)
84865735336757169666…68885087557301196801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.697 × 10⁹⁷(98-digit number)
16973147067351433933…37770175114602393601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.394 × 10⁹⁷(98-digit number)
33946294134702867866…75540350229204787201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.789 × 10⁹⁷(98-digit number)
67892588269405735733…51080700458409574401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.357 × 10⁹⁸(99-digit number)
13578517653881147146…02161400916819148801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.715 × 10⁹⁸(99-digit number)
27157035307762294293…04322801833638297601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.431 × 10⁹⁸(99-digit number)
54314070615524588586…08645603667276595201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.086 × 10⁹⁹(100-digit number)
10862814123104917717…17291207334553190401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.172 × 10⁹⁹(100-digit number)
21725628246209835434…34582414669106380801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.345 × 10⁹⁹(100-digit number)
43451256492419670869…69164829338212761601
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:57,715,010 XPM·at block #6,808,869 · updates every 60s
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