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Block #188,584

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/1/2013, 6:38:36 AM Β· Difficulty 9.8712 Β· 6,607,426 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f503c857cfddab405b10e7618104f2d320fe8c4a667adba328ab34949987688c
View on Chainz β†—

Height

#188,584

Difficulty

9.871236

Transactions

2

Size

427 B

Version

2

Bits

09df0953

Nonce

34,585

Timestamp

10/1/2013, 6:38:36 AM

Confirmations

6,607,426

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

2d426417ec6d3306e5ffdf11f9f2b6421a829c29a5dc16a43683670132d5f44c
Transactions (2)
Coinbaseb850f4bbee3f23…ee16998f4a9a25
1 in β†’ 1 out10.2600 XPM110 B
ANvtpRa1…QjsraDJz
5b8a7a3db5fc57…232724d3a84af6
1 in β†’ 2 out6.2250 XPM227 B
AXwKKGcU…yK2w3TwRAevWi7cv…9THK6EDq
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.

6.161 Γ— 10⁹³(94-digit number)
61617151084458897540…27079225227805658239
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
6.161 Γ— 10⁹³(94-digit number)
61617151084458897540…27079225227805658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁴(95-digit number)
12323430216891779508…54158450455611316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.464 Γ— 10⁹⁴(95-digit number)
24646860433783559016…08316900911222632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.929 Γ— 10⁹⁴(95-digit number)
49293720867567118032…16633801822445265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.858 Γ— 10⁹⁴(95-digit number)
98587441735134236064…33267603644890531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁡(96-digit number)
19717488347026847212…66535207289781063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.943 Γ— 10⁹⁡(96-digit number)
39434976694053694425…33070414579562127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.886 Γ— 10⁹⁡(96-digit number)
78869953388107388851…66140829159124254719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.577 Γ— 10⁹⁢(97-digit number)
15773990677621477770…32281658318248509439
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:57,612,170 XPMΒ·at block #6,796,009 Β· updates every 60s
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