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Block #2,131,578

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/25/2017, 4:50:03 AM Β· Difficulty 10.9104 Β· 4,709,255 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f0ed93ef7168481da8319d80b85b1fcfbfb97edfdc6b66c1c8b04ee433e7eaf9
View on Chainz β†—

Height

#2,131,578

Difficulty

10.910351

Transactions

1

Size

200 B

Version

2

Bits

0ae90cc9

Nonce

431,955,577

Timestamp

5/25/2017, 4:50:03 AM

Confirmations

4,709,255

Mined by

⛏️ P2SHALgrUeweJN4Ak96g1JSXABpK7nRjdWRqH9

Merkle Root

e1a69232d6e19956cb42defc179ddb8ec0acf66d39eceb4bbb239af27bcc809d
Transactions (1)
Coinbasee1a69232d6e199…239af27bcc809d
1 in β†’ 1 out8.3900 XPM109 B
ALgrUewe…RjdWRqH9
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.

1.182 Γ— 10⁹⁢(97-digit number)
11828693443922909528…62288780645725676159
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
1.182 Γ— 10⁹⁢(97-digit number)
11828693443922909528…62288780645725676159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.365 Γ— 10⁹⁢(97-digit number)
23657386887845819057…24577561291451352319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.731 Γ— 10⁹⁢(97-digit number)
47314773775691638114…49155122582902704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.462 Γ— 10⁹⁢(97-digit number)
94629547551383276228…98310245165805409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.892 Γ— 10⁹⁷(98-digit number)
18925909510276655245…96620490331610818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.785 Γ— 10⁹⁷(98-digit number)
37851819020553310491…93240980663221637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.570 Γ— 10⁹⁷(98-digit number)
75703638041106620983…86481961326443274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.514 Γ— 10⁹⁸(99-digit number)
15140727608221324196…72963922652886548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.028 Γ— 10⁹⁸(99-digit number)
30281455216442648393…45927845305773096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.056 Γ— 10⁹⁸(99-digit number)
60562910432885296786…91855690611546193919
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:57,971,010 XPMΒ·at block #6,840,832 Β· updates every 60s
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