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Block #2,679,404

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2018, 11:57:50 PM Β· Difficulty 11.6928 Β· 4,157,125 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a475ad3bf852d5c109139c0956bc5d26416d456b8065795ff290201f48976f7
View on Chainz β†—

Height

#2,679,404

Difficulty

11.692825

Transactions

1

Size

200 B

Version

2

Bits

0bb15d02

Nonce

1,993,041,468

Timestamp

5/26/2018, 11:57:50 PM

Confirmations

4,157,125

Mined by

⛏️ P2SHAJfkXeaVBzs6JNL6mwcQkGsKh179rTp39x

Merkle Root

527a9c5398a09badd9faeae1a0cea7e1eefba07b50f13bbc0db8d097801ae60d
Transactions (1)
Coinbase527a9c5398a09b…b8d097801ae60d
1 in β†’ 1 out7.3000 XPM110 B
AJfkXeaV…79rTp39x
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.

1.875 Γ— 10⁹⁴(95-digit number)
18755442945491889989…55348112381218592799
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
1.875 Γ— 10⁹⁴(95-digit number)
18755442945491889989…55348112381218592799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.751 Γ— 10⁹⁴(95-digit number)
37510885890983779978…10696224762437185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.502 Γ— 10⁹⁴(95-digit number)
75021771781967559957…21392449524874371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁡(96-digit number)
15004354356393511991…42784899049748742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.000 Γ— 10⁹⁡(96-digit number)
30008708712787023982…85569798099497484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.001 Γ— 10⁹⁡(96-digit number)
60017417425574047965…71139596198994969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.200 Γ— 10⁹⁢(97-digit number)
12003483485114809593…42279192397989939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.400 Γ— 10⁹⁢(97-digit number)
24006966970229619186…84558384795979878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.801 Γ— 10⁹⁢(97-digit number)
48013933940459238372…69116769591959756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.602 Γ— 10⁹⁢(97-digit number)
96027867880918476745…38233539183919513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.920 Γ— 10⁹⁷(98-digit number)
19205573576183695349…76467078367839027199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,936,501 XPMΒ·at block #6,836,528 Β· updates every 60s
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