Block #2,644,994

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2018, 5:38:10 PM · Difficulty 11.7225 · 4,188,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a472f791f118fcd1f2c1dd69ac89e01e1e596623bc182ed72d128c771dd952b7

Height

#2,644,994

Difficulty

11.722453

Transactions

7

Size

2.05 KB

Version

2

Bits

0bb8f2ae

Nonce

117,413,933

Timestamp

5/2/2018, 5:38:10 PM

Confirmations

4,188,743

Merkle Root

7872c71712361b159881f4b7f128095f88623b18a19d0a6f9970f26622a600e2
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.

4.481 × 10⁹⁴(95-digit number)
44819867035473045259…29550355679934873601
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
4.481 × 10⁹⁴(95-digit number)
44819867035473045259…29550355679934873601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.963 × 10⁹⁴(95-digit number)
89639734070946090519…59100711359869747201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.792 × 10⁹⁵(96-digit number)
17927946814189218103…18201422719739494401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.585 × 10⁹⁵(96-digit number)
35855893628378436207…36402845439478988801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.171 × 10⁹⁵(96-digit number)
71711787256756872415…72805690878957977601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.434 × 10⁹⁶(97-digit number)
14342357451351374483…45611381757915955201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.868 × 10⁹⁶(97-digit number)
28684714902702748966…91222763515831910401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.736 × 10⁹⁶(97-digit number)
57369429805405497932…82445527031663820801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.147 × 10⁹⁷(98-digit number)
11473885961081099586…64891054063327641601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.294 × 10⁹⁷(98-digit number)
22947771922162199172…29782108126655283201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.589 × 10⁹⁷(98-digit number)
45895543844324398345…59564216253310566401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,914,113 XPM·at block #6,833,736 · updates every 60s
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