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Block #282,366

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/29/2013, 8:58:17 AM Β· Difficulty 9.9790 Β· 6,544,357 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfbd916af388324db0fc428f52aa376d6182d25dcc19350706901ddd1dfb4696
View on Chainz β†—

Height

#282,366

Difficulty

9.978951

Transactions

1

Size

205 B

Version

2

Bits

09fa9c80

Nonce

2,398

Timestamp

11/29/2013, 8:58:17 AM

Confirmations

6,544,357

Merkle Root

c3c27fdb10b7c8c0c060ac13a54eb41e0969ae275e7a322a343f64209842511b
Transactions (1)
Coinbasec3c27fdb10b7c8…3f64209842511b
1 in β†’ 1 out10.0300 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.206 Γ— 10⁹³(94-digit number)
22063348170836946507…30767347160990400160
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
2.206 Γ— 10⁹³(94-digit number)
22063348170836946507…30767347160990400161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.412 Γ— 10⁹³(94-digit number)
44126696341673893015…61534694321980800321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.825 Γ— 10⁹³(94-digit number)
88253392683347786031…23069388643961600641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.765 Γ— 10⁹⁴(95-digit number)
17650678536669557206…46138777287923201281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.530 Γ— 10⁹⁴(95-digit number)
35301357073339114412…92277554575846402561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.060 Γ— 10⁹⁴(95-digit number)
70602714146678228825…84555109151692805121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.412 Γ— 10⁹⁡(96-digit number)
14120542829335645765…69110218303385610241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.824 Γ— 10⁹⁡(96-digit number)
28241085658671291530…38220436606771220481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.648 Γ— 10⁹⁡(96-digit number)
56482171317342583060…76440873213542440961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 282366

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 dfbd916af388324db0fc428f52aa376d6182d25dcc19350706901ddd1dfb4696

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 #282,366 on Chainz β†—
Circulating Supply:57,857,938 XPMΒ·at block #6,826,722 Β· updates every 60s
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