Block #237,999

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2013, 8:19:52 AM · Difficulty 9.9511 · 6,558,681 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6823d1d82f659884e06d1b40d9e9a0ccd86bb1ab80506d0b70fe0b8e5e9e4532

Height

#237,999

Difficulty

9.951090

Transactions

1

Size

2.01 KB

Version

2

Bits

09f37a9c

Nonce

254,902

Timestamp

11/1/2013, 8:19:52 AM

Confirmations

6,558,681

Merkle Root

a5b714c0bbbd1549b2ce5bb607404a107ff16254e4e2fcb3bda964e6f4990157
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.

2.255 × 10⁹⁶(97-digit number)
22555938655747344133…13835858887157233921
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
2.255 × 10⁹⁶(97-digit number)
22555938655747344133…13835858887157233921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.511 × 10⁹⁶(97-digit number)
45111877311494688267…27671717774314467841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.022 × 10⁹⁶(97-digit number)
90223754622989376535…55343435548628935681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.804 × 10⁹⁷(98-digit number)
18044750924597875307…10686871097257871361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.608 × 10⁹⁷(98-digit number)
36089501849195750614…21373742194515742721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.217 × 10⁹⁷(98-digit number)
72179003698391501228…42747484389031485441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.443 × 10⁹⁸(99-digit number)
14435800739678300245…85494968778062970881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.887 × 10⁹⁸(99-digit number)
28871601479356600491…70989937556125941761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.774 × 10⁹⁸(99-digit number)
57743202958713200982…41979875112251883521
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,617,445 XPM·at block #6,796,679 · updates every 60s
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