Block #922,359

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 10:14:57 AM · Difficulty 10.9155 · 5,887,556 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c5f1b0c67a46ef21322e6dee28bb6fd0d79798b372ef6ed1eec5b90f4686c50

Height

#922,359

Difficulty

10.915507

Transactions

5

Size

115.98 KB

Version

2

Bits

0aea5eb0

Nonce

373,975,060

Timestamp

2/4/2015, 10:14:57 AM

Confirmations

5,887,556

Merkle Root

3d949afd5feb491f746d12425f1bacb82d544ecbfd66918e9aa1ad1aa0d6864a
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1078.8587 XPM28.95 KB
200 in → 1 out1031.2701 XPM28.94 KB
200 in → 1 out863.5635 XPM28.94 KB
200 in → 1 out998.4913 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.

9.459 × 10⁹⁵(96-digit number)
94591288429620839027…38665064449156775681
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
9.459 × 10⁹⁵(96-digit number)
94591288429620839027…38665064449156775681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.891 × 10⁹⁶(97-digit number)
18918257685924167805…77330128898313551361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.783 × 10⁹⁶(97-digit number)
37836515371848335610…54660257796627102721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.567 × 10⁹⁶(97-digit number)
75673030743696671221…09320515593254205441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.513 × 10⁹⁷(98-digit number)
15134606148739334244…18641031186508410881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.026 × 10⁹⁷(98-digit number)
30269212297478668488…37282062373016821761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.053 × 10⁹⁷(98-digit number)
60538424594957336977…74564124746033643521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.210 × 10⁹⁸(99-digit number)
12107684918991467395…49128249492067287041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.421 × 10⁹⁸(99-digit number)
24215369837982934790…98256498984134574081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.843 × 10⁹⁸(99-digit number)
48430739675965869581…96512997968269148161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.686 × 10⁹⁸(99-digit number)
96861479351931739163…93025995936538296321
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,723,404 XPM·at block #6,809,914 · updates every 60s
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