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Block #160,128

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/11/2013, 4:51:10 PM Β· Difficulty 9.8618 Β· 6,648,006 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d0c48af3bc08a4e2b5a1265870913c007f9607dc21700b51c84cc0dcd5ae40f2
View on Chainz β†—

Height

#160,128

Difficulty

9.861781

Transactions

1

Size

199 B

Version

2

Bits

09dc9db4

Nonce

213,021

Timestamp

9/11/2013, 4:51:10 PM

Confirmations

6,648,006

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

1c59f50f1e9eec111682ead3d7051a67022a1155e50299c01bbc664151041530
Transactions (1)
Coinbase1c59f50f1e9eec…bc664151041530
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

5.414 Γ— 10⁹³(94-digit number)
54140182122024459797…69063613561677880199
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
5.414 Γ— 10⁹³(94-digit number)
54140182122024459797…69063613561677880199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁴(95-digit number)
10828036424404891959…38127227123355760399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.165 Γ— 10⁹⁴(95-digit number)
21656072848809783919…76254454246711520799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.331 Γ— 10⁹⁴(95-digit number)
43312145697619567838…52508908493423041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.662 Γ— 10⁹⁴(95-digit number)
86624291395239135676…05017816986846083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.732 Γ— 10⁹⁡(96-digit number)
17324858279047827135…10035633973692166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.464 Γ— 10⁹⁡(96-digit number)
34649716558095654270…20071267947384332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.929 Γ— 10⁹⁡(96-digit number)
69299433116191308540…40142535894768665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁢(97-digit number)
13859886623238261708…80285071789537331199
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
Circulating Supply:57,709,114 XPMΒ·at block #6,808,133 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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