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Block #284,441

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/30/2013, 3:16:41 AM Β· Difficulty 9.9827 Β· 6,542,791 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
791ba1d553443aea6f89ea3b9c277410e8acc3a8c484e148965eb6e383a57a57
View on Chainz β†—

Height

#284,441

Difficulty

9.982714

Transactions

1

Size

199 B

Version

2

Bits

09fb9324

Nonce

22,328

Timestamp

11/30/2013, 3:16:41 AM

Confirmations

6,542,791

Mined by

⛏️ P2SHATRnMoWiPfLU4bA2TUCHsxS8iKZP2o2dcV

Merkle Root

40b4b93e08855cc10d3a1b916e6ab236998542ca44f9577d18c0531cc4568911
Transactions (1)
Coinbase40b4b93e08855c…c0531cc4568911
1 in β†’ 1 out10.0200 XPM109 B
ATRnMoWi…ZP2o2dcV
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.

2.340 Γ— 10⁹⁴(95-digit number)
23409745407657195206…78269180455559687499
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
2.340 Γ— 10⁹⁴(95-digit number)
23409745407657195206…78269180455559687499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.681 Γ— 10⁹⁴(95-digit number)
46819490815314390412…56538360911119374999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.363 Γ— 10⁹⁴(95-digit number)
93638981630628780825…13076721822238749999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.872 Γ— 10⁹⁡(96-digit number)
18727796326125756165…26153443644477499999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.745 Γ— 10⁹⁡(96-digit number)
37455592652251512330…52306887288954999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.491 Γ— 10⁹⁡(96-digit number)
74911185304503024660…04613774577909999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.498 Γ— 10⁹⁢(97-digit number)
14982237060900604932…09227549155819999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.996 Γ— 10⁹⁢(97-digit number)
29964474121801209864…18455098311639999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.992 Γ— 10⁹⁢(97-digit number)
59928948243602419728…36910196623279999999
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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
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