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Block #2,643,854

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 6:23:35 AM Β· Difficulty 11.6955 Β· 4,189,956 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09960985f1365b835d050135aaf66368ddb85801d8d889d8e1bd8d5e240f3727
View on Chainz β†—

Height

#2,643,854

Difficulty

11.695471

Transactions

1

Size

201 B

Version

2

Bits

0bb20a6b

Nonce

666,678,938

Timestamp

5/2/2018, 6:23:35 AM

Confirmations

4,189,956

Mined by

⛏️ P2SHALfgL6ZMHg5cKzMvZTdxKwNeCopqyLZCTD

Merkle Root

46e368f1f65fcb7caefc2297aa20361b60a4aa9dee33834a7232bb627150a11e
Transactions (1)
Coinbase46e368f1f65fcb…32bb627150a11e
1 in β†’ 1 out7.3000 XPM110 B
ALfgL6ZM…pqyLZCTD
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.

2.050 Γ— 10⁹⁢(97-digit number)
20501548522143711950…18383090939117598721
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
2.050 Γ— 10⁹⁢(97-digit number)
20501548522143711950…18383090939117598721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.100 Γ— 10⁹⁢(97-digit number)
41003097044287423901…36766181878235197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.200 Γ— 10⁹⁢(97-digit number)
82006194088574847803…73532363756470394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.640 Γ— 10⁹⁷(98-digit number)
16401238817714969560…47064727512940789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.280 Γ— 10⁹⁷(98-digit number)
32802477635429939121…94129455025881579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.560 Γ— 10⁹⁷(98-digit number)
65604955270859878242…88258910051763159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.312 Γ— 10⁹⁸(99-digit number)
13120991054171975648…76517820103526318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.624 Γ— 10⁹⁸(99-digit number)
26241982108343951297…53035640207052636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.248 Γ— 10⁹⁸(99-digit number)
52483964216687902594…06071280414105272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.049 Γ— 10⁹⁹(100-digit number)
10496792843337580518…12142560828210544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.099 Γ— 10⁹⁹(100-digit number)
20993585686675161037…24285121656421089281
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:57,914,704 XPMΒ·at block #6,833,809 Β· updates every 60s
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