Block #492,937

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2014, 10:49:46 AM · Difficulty 10.6919 · 6,303,474 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
330937bce466ecd689816f03fa8390f4b2ae76c1f80ace42f4618b9c112ab5f8

Height

#492,937

Difficulty

10.691946

Transactions

3

Size

3.68 KB

Version

2

Bits

0ab12367

Nonce

366,180,600

Timestamp

4/15/2014, 10:49:46 AM

Confirmations

6,303,474

Merkle Root

3cf1d1f85f441c411de52822340bb69625d033bce558e1a47ab38ac2e8c79c17
Transactions (3)
1 in → 1 out8.7800 XPM109 B
3 in → 1 out27.0100 XPM388 B
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.

8.483 × 10⁹³(94-digit number)
84831823578813536922…49276455430355472211
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
8.483 × 10⁹³(94-digit number)
84831823578813536922…49276455430355472211
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.696 × 10⁹⁴(95-digit number)
16966364715762707384…98552910860710944421
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.393 × 10⁹⁴(95-digit number)
33932729431525414768…97105821721421888841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.786 × 10⁹⁴(95-digit number)
67865458863050829537…94211643442843777681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.357 × 10⁹⁵(96-digit number)
13573091772610165907…88423286885687555361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.714 × 10⁹⁵(96-digit number)
27146183545220331815…76846573771375110721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.429 × 10⁹⁵(96-digit number)
54292367090440663630…53693147542750221441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.085 × 10⁹⁶(97-digit number)
10858473418088132726…07386295085500442881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.171 × 10⁹⁶(97-digit number)
21716946836176265452…14772590171000885761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.343 × 10⁹⁶(97-digit number)
43433893672352530904…29545180342001771521
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:57,615,283 XPM·at block #6,796,410 · updates every 60s
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