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Block #2,649,447

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2018, 6:24:54 AM Β· Difficulty 11.7638 Β· 4,193,381 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
40fe8b4aa74630d52d47f2165449e2d25f72ba82593deee9e4fe3fcafdb26d18
View on Chainz β†—

Height

#2,649,447

Difficulty

11.763829

Transactions

2

Size

392 B

Version

2

Bits

0bc38a4c

Nonce

142,545,561

Timestamp

5/5/2018, 6:24:54 AM

Confirmations

4,193,381

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

923965fe0b030cff7c56994f165ebd7f33970a2a20e0d227b8e860d81ff96a11
Transactions (2)
Coinbaseab4663ce791f52…91541acc3a8e4b
1 in β†’ 1 out7.2300 XPM110 B
Adqah8zh…1WwoHJ9t
96eec3b463057f…e251ca354bec2f
1 in β†’ 2 out7.2100 XPM192 B
AamnkX56…Dk9c6QCrAHvtAN2p…kV7LWUW4
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.

3.672 Γ— 10⁹³(94-digit number)
36727227676601981488…72920401762873913699
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
3.672 Γ— 10⁹³(94-digit number)
36727227676601981488…72920401762873913699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.345 Γ— 10⁹³(94-digit number)
73454455353203962977…45840803525747827399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.469 Γ— 10⁹⁴(95-digit number)
14690891070640792595…91681607051495654799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.938 Γ— 10⁹⁴(95-digit number)
29381782141281585190…83363214102991309599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.876 Γ— 10⁹⁴(95-digit number)
58763564282563170381…66726428205982619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁡(96-digit number)
11752712856512634076…33452856411965238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.350 Γ— 10⁹⁡(96-digit number)
23505425713025268152…66905712823930476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.701 Γ— 10⁹⁡(96-digit number)
47010851426050536305…33811425647860953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.402 Γ— 10⁹⁡(96-digit number)
94021702852101072611…67622851295721907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.880 Γ— 10⁹⁢(97-digit number)
18804340570420214522…35245702591443814399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.760 Γ— 10⁹⁢(97-digit number)
37608681140840429044…70491405182887628799
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:57,986,967 XPMΒ·at block #6,842,827 Β· updates every 60s
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