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Block #145,619

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2013, 12:27:31 AM Β· Difficulty 9.8446 Β· 6,681,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e11422d06f1dd26cff15d20b81aed0cb60520d8de0e559a57a8708acee0848dd
View on Chainz β†—

Height

#145,619

Difficulty

9.844589

Transactions

2

Size

392 B

Version

2

Bits

09d83702

Nonce

36,548

Timestamp

9/2/2013, 12:27:31 AM

Confirmations

6,681,103

Mined by

⛏️ P2SHANxcjsiRs3nPjfibwsj5LZyUCd5w1WUvBK

Merkle Root

89bb3acfcc20fb1de57fc07dcf0ad71b8416cc1bad879014a97ff69d00ce7e40
Transactions (2)
Coinbase02043896e546cb…8ceff14308c12d
1 in β†’ 1 out10.3100 XPM109 B
ANxcjsiR…5w1WUvBK
50d5a1cc714bf9…ba1f3b64383b3b
1 in β†’ 1 out299.9900 XPM193 B
AHUbt4Ww…hcxVK8Cp
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.

3.659 Γ— 10⁹⁡(96-digit number)
36596089259716093894…23613461472685577999
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
3.659 Γ— 10⁹⁡(96-digit number)
36596089259716093894…23613461472685577999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.319 Γ— 10⁹⁡(96-digit number)
73192178519432187789…47226922945371155999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.463 Γ— 10⁹⁢(97-digit number)
14638435703886437557…94453845890742311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.927 Γ— 10⁹⁢(97-digit number)
29276871407772875115…88907691781484623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.855 Γ— 10⁹⁢(97-digit number)
58553742815545750231…77815383562969247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁷(98-digit number)
11710748563109150046…55630767125938495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.342 Γ— 10⁹⁷(98-digit number)
23421497126218300092…11261534251876991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.684 Γ— 10⁹⁷(98-digit number)
46842994252436600185…22523068503753983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.368 Γ— 10⁹⁷(98-digit number)
93685988504873200370…45046137007507967999
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:57,857,930 XPMΒ·at block #6,826,721 Β· updates every 60s
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