Block #2,237,494

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/5/2017, 3:31:27 AM · Difficulty 10.9460 · 4,587,798 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ea727f42460ac97e37da72f0bd0b315e6d28f685e76fd2af1d24a18dd586ba1e

Height

#2,237,494

Difficulty

10.946047

Transactions

3

Size

2.52 KB

Version

2

Bits

0af23023

Nonce

182,213,463

Timestamp

8/5/2017, 3:31:27 AM

Confirmations

4,587,798

Merkle Root

7962bdd294a8af7061311c2114dd25b8a7ba6a854e2259ccde1cf01fa9fffb25
Transactions (3)
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.

1.437 × 10⁹⁶(97-digit number)
14373212551346659724…74889493489600408321
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
1.437 × 10⁹⁶(97-digit number)
14373212551346659724…74889493489600408321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.874 × 10⁹⁶(97-digit number)
28746425102693319449…49778986979200816641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.749 × 10⁹⁶(97-digit number)
57492850205386638899…99557973958401633281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.149 × 10⁹⁷(98-digit number)
11498570041077327779…99115947916803266561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.299 × 10⁹⁷(98-digit number)
22997140082154655559…98231895833606533121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.599 × 10⁹⁷(98-digit number)
45994280164309311119…96463791667213066241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.198 × 10⁹⁷(98-digit number)
91988560328618622238…92927583334426132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.839 × 10⁹⁸(99-digit number)
18397712065723724447…85855166668852264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.679 × 10⁹⁸(99-digit number)
36795424131447448895…71710333337704529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.359 × 10⁹⁸(99-digit number)
73590848262894897790…43420666675409059841
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:57,846,436 XPM·at block #6,825,291 · updates every 60s
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