Block #192,350

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/3/2013, 7:30:00 PM · Difficulty 9.8747 · 6,604,096 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2d511d9f859b3e1255fa3bd8e11a5e3baac815b0832e22b2724e6c2c5e3a6b4

Height

#192,350

Difficulty

9.874736

Transactions

1

Size

3.10 KB

Version

2

Bits

09dfeeb2

Nonce

1,164,774,195

Timestamp

10/3/2013, 7:30:00 PM

Confirmations

6,604,096

Merkle Root

e753c9443c2143442554fc719791fca043f3a11249043c4006eb248837335990
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.

8.349 × 10⁹⁴(95-digit number)
83490076133970895630…11420951929166900569
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
8.349 × 10⁹⁴(95-digit number)
83490076133970895630…11420951929166900569
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.669 × 10⁹⁵(96-digit number)
16698015226794179126…22841903858333801139
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.339 × 10⁹⁵(96-digit number)
33396030453588358252…45683807716667602279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.679 × 10⁹⁵(96-digit number)
66792060907176716504…91367615433335204559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.335 × 10⁹⁶(97-digit number)
13358412181435343300…82735230866670409119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.671 × 10⁹⁶(97-digit number)
26716824362870686601…65470461733340818239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.343 × 10⁹⁶(97-digit number)
53433648725741373203…30940923466681636479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.068 × 10⁹⁷(98-digit number)
10686729745148274640…61881846933363272959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.137 × 10⁹⁷(98-digit number)
21373459490296549281…23763693866726545919
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,615,561 XPM·at block #6,796,445 · updates every 60s
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