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Home/Chain Registry/Block #2,137,766

Block #2,137,766

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/30/2017, 7:54:41 AM Β· Difficulty 10.8866 Β· 4,705,249 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c60246e6345168f4cf4a7801f4cfaa2f0de0609bca79464c1e4bc1b314a7420d
View on Chainz β†—

Difficulty

10.886557

Transactions

1

Size

201 B

Version

2

Bits

0ae2f56b

Nonce

1,067,841,090

Timestamp

5/30/2017, 7:54:41 AM

Confirmations

4,705,249

Merkle Root

1370da5be8209ce7c9eedd52613cfc6bc2f82fdc53de697beeb95be8219d664f
Transactions (1)
Coinbase1370da5be8209c…b95be8219d664f
1 in β†’ 1 out8.4200 XPM110 B
ANZE8Lsn…oo68twxa
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.

7.741 Γ— 10⁹⁡(96-digit number)
77419627882090922770…53084021639152890880
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
7.741 Γ— 10⁹⁡(96-digit number)
77419627882090922770…53084021639152890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15483925576418184554…06168043278305781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.096 Γ— 10⁹⁢(97-digit number)
30967851152836369108…12336086556611563521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.193 Γ— 10⁹⁢(97-digit number)
61935702305672738216…24672173113223127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.238 Γ— 10⁹⁷(98-digit number)
12387140461134547643…49344346226446254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.477 Γ— 10⁹⁷(98-digit number)
24774280922269095286…98688692452892508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.954 Γ— 10⁹⁷(98-digit number)
49548561844538190573…97377384905785016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.909 Γ— 10⁹⁷(98-digit number)
99097123689076381146…94754769811570032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.981 Γ— 10⁹⁸(99-digit number)
19819424737815276229…89509539623140065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.963 Γ— 10⁹⁸(99-digit number)
39638849475630552458…79019079246280130561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2137766

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 c60246e6345168f4cf4a7801f4cfaa2f0de0609bca79464c1e4bc1b314a7420d

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 #2,137,766 on Chainz β†—
Circulating Supply:57,988,475 XPMΒ·at block #6,843,014 Β· updates every 60s
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