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Home/Chain Registry/Block #280,934

Block #280,934

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2013, 8:42:01 PM Β· Difficulty 9.9758 Β· 6,520,086 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
34ffb5efa73ef9fd773131b6c96b436b48fa16ad9c339e90bd93f1e8a0cfaef6
View on Chainz β†—

Height

#280,934

Difficulty

9.975787

Transactions

1

Size

199 B

Version

2

Bits

09f9cd2e

Nonce

96,031

Timestamp

11/28/2013, 8:42:01 PM

Confirmations

6,520,086

Merkle Root

d699c872e8d959a5dd88e612b90611165ebb79997440a2bff2f2389e9a225dc6
Transactions (1)
Coinbased699c872e8d959…f2389e9a225dc6
1 in β†’ 1 out10.0300 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.

1.309 Γ— 10⁹³(94-digit number)
13097514007293321272…94353441139051572300
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
1.309 Γ— 10⁹³(94-digit number)
13097514007293321272…94353441139051572301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.619 Γ— 10⁹³(94-digit number)
26195028014586642545…88706882278103144601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.239 Γ— 10⁹³(94-digit number)
52390056029173285090…77413764556206289201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.047 Γ— 10⁹⁴(95-digit number)
10478011205834657018…54827529112412578401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.095 Γ— 10⁹⁴(95-digit number)
20956022411669314036…09655058224825156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.191 Γ— 10⁹⁴(95-digit number)
41912044823338628072…19310116449650313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.382 Γ— 10⁹⁴(95-digit number)
83824089646677256145…38620232899300627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.676 Γ— 10⁹⁡(96-digit number)
16764817929335451229…77240465798601254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.352 Γ— 10⁹⁡(96-digit number)
33529635858670902458…54480931597202508801
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 280934

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 34ffb5efa73ef9fd773131b6c96b436b48fa16ad9c339e90bd93f1e8a0cfaef6

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 #280,934 on Chainz β†—
Circulating Supply:57,652,222 XPMΒ·at block #6,801,019 Β· updates every 60s
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