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Block #2,822,913

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2018, 2:03:39 PM Β· Difficulty 11.7035 Β· 4,017,847 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2870ce59a8582c561921d8f66844ba2f731ee896246dfa18eba8eadc130e025
View on Chainz β†—

Height

#2,822,913

Difficulty

11.703493

Transactions

1

Size

201 B

Version

2

Bits

0bb4181b

Nonce

37,592,156

Timestamp

9/3/2018, 2:03:39 PM

Confirmations

4,017,847

Mined by

⛏️ P2SHANwPsiVuCskLwvQbjBmRHAP7VvSHzPLjwL

Merkle Root

4a8004bb6f8e422226692696c401cb8cae75d9cb187d369621151007f948853b
Transactions (1)
Coinbase4a8004bb6f8e42…151007f948853b
1 in β†’ 1 out7.2900 XPM110 B
ANwPsiVu…SHzPLjwL
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.

2.667 Γ— 10⁹⁢(97-digit number)
26678857942959491852…91367385157806223361
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
2.667 Γ— 10⁹⁢(97-digit number)
26678857942959491852…91367385157806223361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.335 Γ— 10⁹⁢(97-digit number)
53357715885918983704…82734770315612446721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.067 Γ— 10⁹⁷(98-digit number)
10671543177183796740…65469540631224893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.134 Γ— 10⁹⁷(98-digit number)
21343086354367593481…30939081262449786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.268 Γ— 10⁹⁷(98-digit number)
42686172708735186963…61878162524899573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.537 Γ— 10⁹⁷(98-digit number)
85372345417470373926…23756325049799147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.707 Γ— 10⁹⁸(99-digit number)
17074469083494074785…47512650099598295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.414 Γ— 10⁹⁸(99-digit number)
34148938166988149570…95025300199196590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.829 Γ— 10⁹⁸(99-digit number)
68297876333976299141…90050600398393180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.365 Γ— 10⁹⁹(100-digit number)
13659575266795259828…80101200796786360321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.731 Γ— 10⁹⁹(100-digit number)
27319150533590519656…60202401593572720641
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:57,970,421 XPMΒ·at block #6,840,759 Β· updates every 60s
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