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Block #2,651,027

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 12:35:22 PM Β· Difficulty 11.7526 Β· 4,190,750 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ca3ee4f3e0033878188d54b3591d7a207f32b94a2eeb411e71e75867b69aa37
View on Chainz β†—

Height

#2,651,027

Difficulty

11.752558

Transactions

2

Size

2.15 KB

Version

2

Bits

0bc0a7aa

Nonce

2,116,445,063

Timestamp

5/6/2018, 12:35:22 PM

Confirmations

4,190,750

Mined by

⛏️ P2SHAdfxjyj5STVYLrRVXJkmB569n8RZrQN4b2

Merkle Root

4544a94536887a8984d5117871727dbfafd3a63b24bab76d1b770dd0f024f42c
Transactions (2)
Coinbasecdd84ea354ec1c…5d9e28acb7a0d0
1 in β†’ 1 out7.2600 XPM110 B
Adfxjyj5…RZrQN4b2
fccf584f025231…fd7ee445aa9d22
13 in β†’ 2 out36.6176 XPM1.96 KB
APkJm4hZ…hCC3NPi6AP9s1eRX…C8Rmngfj
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.

1.817 Γ— 10⁹⁢(97-digit number)
18179335042332588893…87336720200315050401
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
1.817 Γ— 10⁹⁢(97-digit number)
18179335042332588893…87336720200315050401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.635 Γ— 10⁹⁢(97-digit number)
36358670084665177787…74673440400630100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.271 Γ— 10⁹⁢(97-digit number)
72717340169330355575…49346880801260201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.454 Γ— 10⁹⁷(98-digit number)
14543468033866071115…98693761602520403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.908 Γ— 10⁹⁷(98-digit number)
29086936067732142230…97387523205040806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.817 Γ— 10⁹⁷(98-digit number)
58173872135464284460…94775046410081612801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.163 Γ— 10⁹⁸(99-digit number)
11634774427092856892…89550092820163225601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.326 Γ— 10⁹⁸(99-digit number)
23269548854185713784…79100185640326451201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.653 Γ— 10⁹⁸(99-digit number)
46539097708371427568…58200371280652902401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.307 Γ— 10⁹⁸(99-digit number)
93078195416742855136…16400742561305804801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.861 Γ— 10⁹⁹(100-digit number)
18615639083348571027…32801485122611609601
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:57,978,592 XPMΒ·at block #6,841,776 Β· updates every 60s
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