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Block #223,093

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 5:44:18 PM Β· Difficulty 9.9389 Β· 6,587,242 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
42cb471d7a4f78acbb60fa4e9adfa54ed7da7a5953a30befb9c90c5bf2e2e7b6
View on Chainz β†—

Height

#223,093

Difficulty

9.938871

Transactions

1

Size

206 B

Version

2

Bits

09f059e1

Nonce

67,109,822

Timestamp

10/22/2013, 5:44:18 PM

Confirmations

6,587,242

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

49f1448408209cb4269e6470846059f0b1565e3320fe08018357e9cb7283f63d
Transactions (1)
Coinbase49f1448408209c…57e9cb7283f63d
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.049 Γ— 10⁹⁡(96-digit number)
10497556294951889300…64811284918369390269
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.049 Γ— 10⁹⁡(96-digit number)
10497556294951889300…64811284918369390269
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.099 Γ— 10⁹⁡(96-digit number)
20995112589903778601…29622569836738780539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.199 Γ— 10⁹⁡(96-digit number)
41990225179807557202…59245139673477561079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.398 Γ— 10⁹⁡(96-digit number)
83980450359615114405…18490279346955122159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁢(97-digit number)
16796090071923022881…36980558693910244319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.359 Γ— 10⁹⁢(97-digit number)
33592180143846045762…73961117387820488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.718 Γ— 10⁹⁢(97-digit number)
67184360287692091524…47922234775640977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁷(98-digit number)
13436872057538418304…95844469551281954559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.687 Γ— 10⁹⁷(98-digit number)
26873744115076836609…91688939102563909119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.374 Γ— 10⁹⁷(98-digit number)
53747488230153673219…83377878205127818239
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,726,761 XPMΒ·at block #6,810,334 Β· updates every 60s
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