Block #922,382

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 10:40:20 AM · Difficulty 10.9155 · 5,873,281 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d19f0bd92b1444810487fd705d6817240806fb5bc983817c074825e9b2a28557

Height

#922,382

Difficulty

10.915531

Transactions

5

Size

115.99 KB

Version

2

Bits

0aea6039

Nonce

497,943,020

Timestamp

2/4/2015, 10:40:20 AM

Confirmations

5,873,281

Merkle Root

06bf84141282e2ff36def1f3d80bc0e5f3f78df28b3525b06478e47ebefe9a5f
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out988.3002 XPM28.96 KB
200 in → 1 out980.5780 XPM28.94 KB
200 in → 1 out1093.2843 XPM28.94 KB
200 in → 1 out1057.4256 XPM28.94 KB
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.

4.179 × 10⁹⁴(95-digit number)
41798565551096801116…89189027207818815441
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
4.179 × 10⁹⁴(95-digit number)
41798565551096801116…89189027207818815441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.359 × 10⁹⁴(95-digit number)
83597131102193602233…78378054415637630881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.671 × 10⁹⁵(96-digit number)
16719426220438720446…56756108831275261761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.343 × 10⁹⁵(96-digit number)
33438852440877440893…13512217662550523521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.687 × 10⁹⁵(96-digit number)
66877704881754881786…27024435325101047041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.337 × 10⁹⁶(97-digit number)
13375540976350976357…54048870650202094081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.675 × 10⁹⁶(97-digit number)
26751081952701952714…08097741300404188161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.350 × 10⁹⁶(97-digit number)
53502163905403905429…16195482600808376321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.070 × 10⁹⁷(98-digit number)
10700432781080781085…32390965201616752641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.140 × 10⁹⁷(98-digit number)
21400865562161562171…64781930403233505281
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:57,609,376 XPM·at block #6,795,662 · updates every 60s
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