Block #922,418

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 11:18:03 AM · Difficulty 10.9154 · 5,886,817 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d94c10bb9ab3f8b87760e975d190a5c472e89008ba696f6dab993f67bd2eb348

Height

#922,418

Difficulty

10.915425

Transactions

5

Size

115.96 KB

Version

2

Bits

0aea594f

Nonce

3,319,253,348

Timestamp

2/4/2015, 11:18:03 AM

Confirmations

5,886,817

Merkle Root

96de33c66fa754d8154c835acddea28582777d8b1e1afc08b8f62b684024ce70
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1053.0101 XPM28.96 KB
200 in → 1 out1031.9232 XPM28.93 KB
200 in → 1 out997.3136 XPM28.93 KB
200 in → 1 out1017.2313 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.

2.106 × 10⁹²(93-digit number)
21063322836699468093…48889788165946610599
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
2.106 × 10⁹²(93-digit number)
21063322836699468093…48889788165946610599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.212 × 10⁹²(93-digit number)
42126645673398936187…97779576331893221199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.425 × 10⁹²(93-digit number)
84253291346797872375…95559152663786442399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.685 × 10⁹³(94-digit number)
16850658269359574475…91118305327572884799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.370 × 10⁹³(94-digit number)
33701316538719148950…82236610655145769599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.740 × 10⁹³(94-digit number)
67402633077438297900…64473221310291539199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.348 × 10⁹⁴(95-digit number)
13480526615487659580…28946442620583078399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.696 × 10⁹⁴(95-digit number)
26961053230975319160…57892885241166156799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.392 × 10⁹⁴(95-digit number)
53922106461950638320…15785770482332313599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.078 × 10⁹⁵(96-digit number)
10784421292390127664…31571540964664627199
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,717,944 XPM·at block #6,809,234 · updates every 60s
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