Block #922,419

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 11:19:45 AM · Difficulty 10.9154 · 5,873,463 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0fa566aadb10dc1dc2f8f9140ea8622d44e1b789bd2886ce24ae33800a9b95fe

Height

#922,419

Difficulty

10.915438

Transactions

5

Size

115.97 KB

Version

2

Bits

0aea5a23

Nonce

1,035,919,235

Timestamp

2/4/2015, 11:19:45 AM

Confirmations

5,873,463

Merkle Root

0846c02f98829d9f41b0833e681c993259e7abea86cf9f1805d0c2e6194ea8c7
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1091.4331 XPM28.95 KB
200 in → 1 out1065.3284 XPM28.93 KB
200 in → 1 out948.9844 XPM28.94 KB
200 in → 1 out1042.6188 XPM28.95 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.

6.769 × 10⁹³(94-digit number)
67695568864904884186…91848865447379623601
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
6.769 × 10⁹³(94-digit number)
67695568864904884186…91848865447379623601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.353 × 10⁹⁴(95-digit number)
13539113772980976837…83697730894759247201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.707 × 10⁹⁴(95-digit number)
27078227545961953674…67395461789518494401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.415 × 10⁹⁴(95-digit number)
54156455091923907349…34790923579036988801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.083 × 10⁹⁵(96-digit number)
10831291018384781469…69581847158073977601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.166 × 10⁹⁵(96-digit number)
21662582036769562939…39163694316147955201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.332 × 10⁹⁵(96-digit number)
43325164073539125879…78327388632295910401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.665 × 10⁹⁵(96-digit number)
86650328147078251759…56654777264591820801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.733 × 10⁹⁶(97-digit number)
17330065629415650351…13309554529183641601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.466 × 10⁹⁶(97-digit number)
34660131258831300703…26619109058367283201
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:57,611,146 XPM·at block #6,795,881 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.