Block #184,380

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/28/2013, 3:27:19 PM · Difficulty 9.8594 · 6,619,336 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dfc1644c7eb0204db2b9622543d1f6fcd863c7ce226336f0869420a310a83923

Height

#184,380

Difficulty

9.859402

Transactions

2

Size

425 B

Version

2

Bits

09dc01c7

Nonce

110,288

Timestamp

9/28/2013, 3:27:19 PM

Confirmations

6,619,336

Merkle Root

dc61371add86a480245dc375b4c0c362da87065f9d1c620734ef7b472cc8398f
Transactions (2)
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.

1.092 × 10⁹⁵(96-digit number)
10922213699721007564…20694836985592709119
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
1.092 × 10⁹⁵(96-digit number)
10922213699721007564…20694836985592709119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.184 × 10⁹⁵(96-digit number)
21844427399442015128…41389673971185418239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.368 × 10⁹⁵(96-digit number)
43688854798884030257…82779347942370836479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.737 × 10⁹⁵(96-digit number)
87377709597768060515…65558695884741672959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.747 × 10⁹⁶(97-digit number)
17475541919553612103…31117391769483345919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.495 × 10⁹⁶(97-digit number)
34951083839107224206…62234783538966691839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.990 × 10⁹⁶(97-digit number)
69902167678214448412…24469567077933383679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.398 × 10⁹⁷(98-digit number)
13980433535642889682…48939134155866767359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.796 × 10⁹⁷(98-digit number)
27960867071285779364…97878268311733534719
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:57,673,769 XPM·at block #6,803,715 · updates every 60s
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