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Block #151,055

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 10:46:53 AM Β· Difficulty 9.8595 Β· 6,654,119 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5452367ce6b4e0fd77938e68135259e55d3658619d7a32fd9cc86b32b383dac3
View on Chainz β†—

Height

#151,055

Difficulty

9.859502

Transactions

1

Size

198 B

Version

2

Bits

09dc0850

Nonce

171,034

Timestamp

9/5/2013, 10:46:53 AM

Confirmations

6,654,119

Mined by

⛏️ P2SHAPK6TsLc8JxWgj41xMVz2y8mnfkbATRbnm

Merkle Root

c94fd08ec6c1556a72e9782191cfd34d560f846eb5d46e1eec4a57c2a143a79b
Transactions (1)
Coinbasec94fd08ec6c155…4a57c2a143a79b
1 in β†’ 1 out10.2700 XPM109 B
APK6TsLc…kbATRbnm
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.

1.638 Γ— 10⁹³(94-digit number)
16384506797152505700…96647009539998974979
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
1.638 Γ— 10⁹³(94-digit number)
16384506797152505700…96647009539998974979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.276 Γ— 10⁹³(94-digit number)
32769013594305011400…93294019079997949959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.553 Γ— 10⁹³(94-digit number)
65538027188610022800…86588038159995899919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁴(95-digit number)
13107605437722004560…73176076319991799839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.621 Γ— 10⁹⁴(95-digit number)
26215210875444009120…46352152639983599679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.243 Γ— 10⁹⁴(95-digit number)
52430421750888018240…92704305279967199359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁡(96-digit number)
10486084350177603648…85408610559934398719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.097 Γ— 10⁹⁡(96-digit number)
20972168700355207296…70817221119868797439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.194 Γ— 10⁹⁡(96-digit number)
41944337400710414592…41634442239737594879
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:57,685,460 XPMΒ·at block #6,805,173 Β· updates every 60s
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