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Block #189,782

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/2/2013, 12:59:39 AM Β· Difficulty 9.8739 Β· 6,608,952 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a22b383f27fa691759cfe84575750a02b4f10d114880e29ee9c7fed837267a8
View on Chainz β†—

Height

#189,782

Difficulty

9.873918

Transactions

2

Size

1.68 KB

Version

2

Bits

09dfb918

Nonce

354,450

Timestamp

10/2/2013, 12:59:39 AM

Confirmations

6,608,952

Mined by

⛏️ P2SHAJHy63jeXcWP53SoT3cmtwSrEvgcpU5UnY

Merkle Root

2226e7f546bc16fc001402e2f8de1ba9aad3f2065470172ed3c3a26e5fa7f171
Transactions (2)
Coinbase643d8e90b20737…b136783b01f25e
1 in β†’ 1 out10.2600 XPM109 B
AJHy63je…gcpU5UnY
df50ca097d233e…400088d57a6031
13 in β†’ 1 out133.5900 XPM1.49 KB
AaZTHvEh…QXHS2iBB
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.

1.385 Γ— 10⁹³(94-digit number)
13859139291137651041…00914450362595861759
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
1.385 Γ— 10⁹³(94-digit number)
13859139291137651041…00914450362595861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.771 Γ— 10⁹³(94-digit number)
27718278582275302082…01828900725191723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.543 Γ— 10⁹³(94-digit number)
55436557164550604165…03657801450383447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁴(95-digit number)
11087311432910120833…07315602900766894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.217 Γ— 10⁹⁴(95-digit number)
22174622865820241666…14631205801533788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.434 Γ— 10⁹⁴(95-digit number)
44349245731640483332…29262411603067576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.869 Γ— 10⁹⁴(95-digit number)
88698491463280966664…58524823206135152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.773 Γ— 10⁹⁡(96-digit number)
17739698292656193332…17049646412270305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.547 Γ— 10⁹⁡(96-digit number)
35479396585312386665…34099292824540610559
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:57,633,896 XPMΒ·at block #6,798,733 Β· updates every 60s
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