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Block #2,822,762

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2018, 11:43:32 AM Β· Difficulty 11.7029 Β· 4,016,052 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ebfd05af4e5f2aeb5d06343528663ed7fa70293bb6f70a05d8f68bf488c7336
View on Chainz β†—

Height

#2,822,762

Difficulty

11.702857

Transactions

2

Size

3.16 KB

Version

2

Bits

0bb3ee6c

Nonce

1,394,557,126

Timestamp

9/3/2018, 11:43:32 AM

Confirmations

4,016,052

Mined by

⛏️ P2SHASMzgrnbfxAdfnH2DaViGGzgx11eN5ZxEM

Merkle Root

cfd901023d4d55378c385675d08f6f282423d07833c96bb1582120e275ec9e3c
Transactions (2)
Coinbase37ddfaa464c59f…ab9fe6470db141
1 in β†’ 1 out7.3300 XPM110 B
ASMzgrnb…1eN5ZxEM
180278fb492a0e…c71689f6b5254a
20 in β†’ 2 out199.9600 XPM2.96 KB
AK4BX2ff…KQZYCU1MALh5G3Np…6TsNC2wj
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.

2.861 Γ— 10⁹⁡(96-digit number)
28614199487336657344…56488902787642149761
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.861 Γ— 10⁹⁡(96-digit number)
28614199487336657344…56488902787642149761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.722 Γ— 10⁹⁡(96-digit number)
57228398974673314689…12977805575284299521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.144 Γ— 10⁹⁢(97-digit number)
11445679794934662937…25955611150568599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.289 Γ— 10⁹⁢(97-digit number)
22891359589869325875…51911222301137198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.578 Γ— 10⁹⁢(97-digit number)
45782719179738651751…03822444602274396161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.156 Γ— 10⁹⁢(97-digit number)
91565438359477303502…07644889204548792321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.831 Γ— 10⁹⁷(98-digit number)
18313087671895460700…15289778409097584641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.662 Γ— 10⁹⁷(98-digit number)
36626175343790921401…30579556818195169281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.325 Γ— 10⁹⁷(98-digit number)
73252350687581842802…61159113636390338561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.465 Γ— 10⁹⁸(99-digit number)
14650470137516368560…22318227272780677121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.930 Γ— 10⁹⁸(99-digit number)
29300940275032737120…44636454545561354241
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,954,777 XPMΒ·at block #6,838,813 Β· updates every 60s
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