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Block #285,549

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 1:04:59 PM Β· Difficulty 9.9844 Β· 6,528,527 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3485f4ca09dc0c7611501a943091c5eafca34b374845ea09322f806dceb47c78
View on Chainz β†—

Height

#285,549

Difficulty

9.984447

Transactions

1

Size

200 B

Version

2

Bits

09fc04b6

Nonce

2,108

Timestamp

11/30/2013, 1:04:59 PM

Confirmations

6,528,527

Merkle Root

8518a7dd59342bd8c8f08adbd905afc6a40e8dab9e07fc4b724186fe2a3e4b11
Transactions (1)
Coinbase8518a7dd59342b…4186fe2a3e4b11
1 in β†’ 1 out10.0200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.684 Γ— 10⁹⁡(96-digit number)
36840457194322825789…80060632637165880320
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
3.684 Γ— 10⁹⁡(96-digit number)
36840457194322825789…80060632637165880321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.368 Γ— 10⁹⁡(96-digit number)
73680914388645651578…60121265274331760641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.473 Γ— 10⁹⁢(97-digit number)
14736182877729130315…20242530548663521281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.947 Γ— 10⁹⁢(97-digit number)
29472365755458260631…40485061097327042561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.894 Γ— 10⁹⁢(97-digit number)
58944731510916521262…80970122194654085121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.178 Γ— 10⁹⁷(98-digit number)
11788946302183304252…61940244389308170241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.357 Γ— 10⁹⁷(98-digit number)
23577892604366608505…23880488778616340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.715 Γ— 10⁹⁷(98-digit number)
47155785208733217010…47760977557232680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.431 Γ— 10⁹⁷(98-digit number)
94311570417466434020…95521955114465361921
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 285549

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 3485f4ca09dc0c7611501a943091c5eafca34b374845ea09322f806dceb47c78

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 #285,549 on Chainz β†—
Circulating Supply:57,756,688 XPMΒ·at block #6,814,075 Β· updates every 60s
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