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Home/Chain Registry/Block #2,682,866

Block #2,682,866

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/29/2018, 10:18:15 AM Β· Difficulty 11.6906 Β· 4,162,087 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac723bd8bc902fa1db13404981850527a1c39cd4892d98eff892793ff75cafa0
View on Chainz β†—

Difficulty

11.690607

Transactions

1

Size

200 B

Version

2

Bits

0bb0cba1

Nonce

728,868,128

Timestamp

5/29/2018, 10:18:15 AM

Confirmations

4,162,087

Merkle Root

a44d22459393d8e5bd3f5a5a284867991592bcaf60a835605e1256166f862e98
Transactions (1)
Coinbasea44d22459393d8…1256166f862e98
1 in β†’ 1 out7.3000 XPM110 B
AUTR5iMm…puLU5idu
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.

5.140 Γ— 10⁹⁴(95-digit number)
51404753701910329485…48297218191595335120
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
5.140 Γ— 10⁹⁴(95-digit number)
51404753701910329485…48297218191595335121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.028 Γ— 10⁹⁡(96-digit number)
10280950740382065897…96594436383190670241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.056 Γ— 10⁹⁡(96-digit number)
20561901480764131794…93188872766381340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.112 Γ— 10⁹⁡(96-digit number)
41123802961528263588…86377745532762680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.224 Γ— 10⁹⁡(96-digit number)
82247605923056527177…72755491065525361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.644 Γ— 10⁹⁢(97-digit number)
16449521184611305435…45510982131050723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.289 Γ— 10⁹⁢(97-digit number)
32899042369222610870…91021964262101447681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.579 Γ— 10⁹⁢(97-digit number)
65798084738445221741…82043928524202895361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.315 Γ— 10⁹⁷(98-digit number)
13159616947689044348…64087857048405790721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.631 Γ— 10⁹⁷(98-digit number)
26319233895378088696…28175714096811581441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.263 Γ— 10⁹⁷(98-digit number)
52638467790756177393…56351428193623162881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.052 Γ— 10⁹⁸(99-digit number)
10527693558151235478…12702856387246325761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2682866

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock ac723bd8bc902fa1db13404981850527a1c39cd4892d98eff892793ff75cafa0

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,682,866 on Chainz β†—
Circulating Supply:58,004,041 XPMΒ·at block #6,844,952 Β· updates every 60s
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