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Home/Chain Registry/Block #1,350,166

Block #1,350,166

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2015, 7:55:17 PM Β· Difficulty 10.8043 Β· 5,445,630 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
af28c792c413462c91f0f47c3a69f8efdb83b54fbc4212f10988bcf91fe41bdd
View on Chainz β†—

Difficulty

10.804306

Transactions

1

Size

200 B

Version

2

Bits

0acde6f9

Nonce

2,025,859,263

Timestamp

12/1/2015, 7:55:17 PM

Confirmations

5,445,630

Merkle Root

ae55d0e3423f27a8fe8c542ceb8d3ee75a22c1f971044e27ffa1419ba8242086
Transactions (1)
Coinbaseae55d0e3423f27…a1419ba8242086
1 in β†’ 1 out8.5500 XPM109 B
AXEoHpsp…M7ZijNb1
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.

3.883 Γ— 10⁹⁢(97-digit number)
38830166126629698055…25946708350445731840
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
3.883 Γ— 10⁹⁢(97-digit number)
38830166126629698055…25946708350445731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.766 Γ— 10⁹⁢(97-digit number)
77660332253259396111…51893416700891463681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.553 Γ— 10⁹⁷(98-digit number)
15532066450651879222…03786833401782927361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.106 Γ— 10⁹⁷(98-digit number)
31064132901303758444…07573666803565854721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.212 Γ— 10⁹⁷(98-digit number)
62128265802607516889…15147333607131709441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.242 Γ— 10⁹⁸(99-digit number)
12425653160521503377…30294667214263418881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.485 Γ— 10⁹⁸(99-digit number)
24851306321043006755…60589334428526837761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.970 Γ— 10⁹⁸(99-digit number)
49702612642086013511…21178668857053675521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.940 Γ— 10⁹⁸(99-digit number)
99405225284172027023…42357337714107351041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.988 Γ— 10⁹⁹(100-digit number)
19881045056834405404…84714675428214702081
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 1350166

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 af28c792c413462c91f0f47c3a69f8efdb83b54fbc4212f10988bcf91fe41bdd

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 #1,350,166 on Chainz β†—
Circulating Supply:57,610,447 XPMΒ·at block #6,795,795 Β· updates every 60s
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