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Block #511,929

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/26/2014, 1:35:39 PM Β· Difficulty 10.8315 Β· 6,292,004 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ae5cc0d1e7f622e442c26625bf10c4ae13e390bfa6fcfe79432a0570765e354
View on Chainz β†—

Height

#511,929

Difficulty

10.831473

Transactions

1

Size

189 B

Version

2

Bits

0ad4db66

Nonce

10,512,325

Timestamp

4/26/2014, 1:35:39 PM

Confirmations

6,292,004

Mined by

⛏️ JASCnrG3mLkjr3GpWyPXMWz8LQ84bFe7YLG

Merkle Root

dd3bc8f88e96b139030ff45914ee975d292e670437f947d87cd619ac5e271a64
Transactions (1)
Coinbasedd3bc8f88e96b1…d619ac5e271a64
1 in β†’ 1 out8.5100 XPM93 B
ASCnrG3m…4bFe7YLG
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.

1.625 Γ— 10¹⁰⁸(109-digit number)
16256083227807974605…84546281528342824079
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
1.625 Γ— 10¹⁰⁸(109-digit number)
16256083227807974605…84546281528342824079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.251 Γ— 10¹⁰⁸(109-digit number)
32512166455615949211…69092563056685648159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.502 Γ— 10¹⁰⁸(109-digit number)
65024332911231898423…38185126113371296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.300 Γ— 10¹⁰⁹(110-digit number)
13004866582246379684…76370252226742592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.600 Γ— 10¹⁰⁹(110-digit number)
26009733164492759369…52740504453485185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.201 Γ— 10¹⁰⁹(110-digit number)
52019466328985518738…05481008906970370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.040 Γ— 10¹¹⁰(111-digit number)
10403893265797103747…10962017813940741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.080 Γ— 10¹¹⁰(111-digit number)
20807786531594207495…21924035627881482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.161 Γ— 10¹¹⁰(111-digit number)
41615573063188414991…43848071255762964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.323 Γ— 10¹¹⁰(111-digit number)
83231146126376829982…87696142511525928959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,675,514 XPMΒ·at block #6,803,932 Β· updates every 60s
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