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Block #201,912

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/9/2013, 9:54:27 PM Β· Difficulty 9.8937 Β· 6,625,009 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee100d681b033d367c1f01c0b0a57b56cbda93fd61e757e1d7534f935e58b2e9
View on Chainz β†—

Height

#201,912

Difficulty

9.893708

Transactions

1

Size

204 B

Version

2

Bits

09e4ca13

Nonce

33,555,137

Timestamp

10/9/2013, 9:54:27 PM

Confirmations

6,625,009

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f20571add12e15d65cb17ba6b11d1253ef6cd1260dffb341ba96e7f9add96bdf
Transactions (1)
Coinbasef20571add12e15…96e7f9add96bdf
1 in β†’ 1 out10.2000 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.

1.992 Γ— 10⁹⁰(91-digit number)
19924371220004265892…87536445600096359999
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
1.992 Γ— 10⁹⁰(91-digit number)
19924371220004265892…87536445600096359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.984 Γ— 10⁹⁰(91-digit number)
39848742440008531784…75072891200192719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.969 Γ— 10⁹⁰(91-digit number)
79697484880017063568…50145782400385439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.593 Γ— 10⁹¹(92-digit number)
15939496976003412713…00291564800770879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.187 Γ— 10⁹¹(92-digit number)
31878993952006825427…00583129601541759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.375 Γ— 10⁹¹(92-digit number)
63757987904013650854…01166259203083519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.275 Γ— 10⁹²(93-digit number)
12751597580802730170…02332518406167039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.550 Γ— 10⁹²(93-digit number)
25503195161605460341…04665036812334079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.100 Γ— 10⁹²(93-digit number)
51006390323210920683…09330073624668159999
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:57,859,539 XPMΒ·at block #6,826,920 Β· updates every 60s
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