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Block #1,755,027

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2016, 2:33:05 PM Β· Difficulty 10.7061 Β· 5,051,729 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
212adb00e79dd04cd1e704f3182681deae074125eb16d9a46bc35cb18c5d3dd3
View on Chainz β†—

Height

#1,755,027

Difficulty

10.706095

Transactions

2

Size

38.13 KB

Version

2

Bits

0ab4c2a8

Nonce

312,692,485

Timestamp

9/9/2016, 2:33:05 PM

Confirmations

5,051,729

Mined by

⛏️ P2SHAUK47tnY1ixdW7X6gWqh8vJBzfad24kLH5

Merkle Root

b7b52fe10deeac7c478f669f5a8aaae256fced08631b9f686bf41076488ae187
Transactions (2)
Coinbased37adb9335a868…61770046e2ffb9
1 in β†’ 1 out9.1800 XPM109 B
AUK47tnY…ad24kLH5
c3b8adcce34a40…59c167add38aae
262 in β†’ 2 out50000.0100 XPM37.94 KB
AYKArr5V…V9VqiqCZAM1pWu42…ayTiVTn5
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.

1.578 Γ— 10⁹⁢(97-digit number)
15780296978753487418…87019264504620083199
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
1.578 Γ— 10⁹⁢(97-digit number)
15780296978753487418…87019264504620083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.156 Γ— 10⁹⁢(97-digit number)
31560593957506974837…74038529009240166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.312 Γ— 10⁹⁢(97-digit number)
63121187915013949675…48077058018480332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.262 Γ— 10⁹⁷(98-digit number)
12624237583002789935…96154116036960665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.524 Γ— 10⁹⁷(98-digit number)
25248475166005579870…92308232073921331199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.049 Γ— 10⁹⁷(98-digit number)
50496950332011159740…84616464147842662399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁸(99-digit number)
10099390066402231948…69232928295685324799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.019 Γ— 10⁹⁸(99-digit number)
20198780132804463896…38465856591370649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.039 Γ— 10⁹⁸(99-digit number)
40397560265608927792…76931713182741299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.079 Γ— 10⁹⁸(99-digit number)
80795120531217855585…53863426365482598399
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:57,698,147 XPMΒ·at block #6,806,755 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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