Block #922,324

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 9:35:14 AM · Difficulty 10.9156 · 5,887,330 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b867dfb0a160dd74397d1192c49fd95e6201f5d00fbe36deed662ce306e41e92

Height

#922,324

Difficulty

10.915569

Transactions

5

Size

115.98 KB

Version

2

Bits

0aea62c1

Nonce

287,379,922

Timestamp

2/4/2015, 9:35:14 AM

Confirmations

5,887,330

Merkle Root

26a872b888b2820773af6b36a1cea9546c93caf8505eef933e5a136fb53efb10
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1128.2408 XPM28.95 KB
200 in → 1 out1040.5472 XPM28.94 KB
200 in → 1 out1125.7580 XPM28.94 KB
200 in → 1 out1081.8914 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.

5.199 × 10⁹⁴(95-digit number)
51994651494601217651…51638060434875348921
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
5.199 × 10⁹⁴(95-digit number)
51994651494601217651…51638060434875348921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.039 × 10⁹⁵(96-digit number)
10398930298920243530…03276120869750697841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.079 × 10⁹⁵(96-digit number)
20797860597840487060…06552241739501395681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.159 × 10⁹⁵(96-digit number)
41595721195680974121…13104483479002791361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.319 × 10⁹⁵(96-digit number)
83191442391361948242…26208966958005582721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.663 × 10⁹⁶(97-digit number)
16638288478272389648…52417933916011165441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.327 × 10⁹⁶(97-digit number)
33276576956544779296…04835867832022330881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.655 × 10⁹⁶(97-digit number)
66553153913089558593…09671735664044661761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.331 × 10⁹⁷(98-digit number)
13310630782617911718…19343471328089323521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.662 × 10⁹⁷(98-digit number)
26621261565235823437…38686942656178647041
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:57,721,313 XPM·at block #6,809,653 · updates every 60s
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