Block #922,363

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 10:17:09 AM · Difficulty 10.9155 · 5,869,619 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
63afef1ca3906aa13ac8c3df3379a96c7cd342a0e02c81d8d82c4e5670cd3746

Height

#922,363

Difficulty

10.915512

Transactions

5

Size

115.99 KB

Version

2

Bits

0aea5efd

Nonce

1,164,389,869

Timestamp

2/4/2015, 10:17:09 AM

Confirmations

5,869,619

Merkle Root

a7b8b4d59467790121365b4db4e253a1b4dfdd62b077a9c5c4ea02ec491bc446
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1021.0267 XPM28.96 KB
200 in → 1 out976.4672 XPM28.93 KB
200 in → 1 out989.0569 XPM28.95 KB
200 in → 1 out909.8624 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.

1.946 × 10⁹⁶(97-digit number)
19469859999371272665…16377672924197817921
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
1.946 × 10⁹⁶(97-digit number)
19469859999371272665…16377672924197817921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.893 × 10⁹⁶(97-digit number)
38939719998742545330…32755345848395635841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.787 × 10⁹⁶(97-digit number)
77879439997485090661…65510691696791271681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.557 × 10⁹⁷(98-digit number)
15575887999497018132…31021383393582543361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.115 × 10⁹⁷(98-digit number)
31151775998994036264…62042766787165086721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.230 × 10⁹⁷(98-digit number)
62303551997988072529…24085533574330173441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.246 × 10⁹⁸(99-digit number)
12460710399597614505…48171067148660346881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.492 × 10⁹⁸(99-digit number)
24921420799195229011…96342134297320693761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.984 × 10⁹⁸(99-digit number)
49842841598390458023…92684268594641387521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.968 × 10⁹⁸(99-digit number)
99685683196780916046…85368537189282775041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.993 × 10⁹⁹(100-digit number)
19937136639356183209…70737074378565550081
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:57,579,817 XPM·at block #6,791,981 · updates every 60s
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