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Block #281,090

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 9:54:56 PM Β· Difficulty 9.9762 Β· 6,523,699 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d41e24a535afa740bc691d2584b1fa665202e7b470a4165664bdaaa9f22ced71
View on Chainz β†—

Height

#281,090

Difficulty

9.976189

Transactions

1

Size

1.18 KB

Version

2

Bits

09f9e78e

Nonce

265,090

Timestamp

11/28/2013, 9:54:56 PM

Confirmations

6,523,699

Merkle Root

7f452aad14d5372caaaa3cb3c145f76bedaf03fed0b435d13edd9bbd644b0c10
Transactions (1)
Coinbase7f452aad14d537…dd9bbd644b0c10
1 in β†’ 31 out10.0100 XPM1.09 KB
AVss9H5F…zXhyMijYAN63YyQR…1tfe566AAHLsU39G…fiNcno66AYrgZtF4…6oLCC7XKAHV2J3tP…7ZwLJbDZ
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.

4.091 Γ— 10⁹⁴(95-digit number)
40916853197128942636…16051486647937074240
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.091 Γ— 10⁹⁴(95-digit number)
40916853197128942636…16051486647937074239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.183 Γ— 10⁹⁴(95-digit number)
81833706394257885273…32102973295874148479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.636 Γ— 10⁹⁡(96-digit number)
16366741278851577054…64205946591748296959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.273 Γ— 10⁹⁡(96-digit number)
32733482557703154109…28411893183496593919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.546 Γ— 10⁹⁡(96-digit number)
65466965115406308219…56823786366993187839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.309 Γ— 10⁹⁢(97-digit number)
13093393023081261643…13647572733986375679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.618 Γ— 10⁹⁢(97-digit number)
26186786046162523287…27295145467972751359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.237 Γ— 10⁹⁢(97-digit number)
52373572092325046575…54590290935945502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁷(98-digit number)
10474714418465009315…09180581871891005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.094 Γ— 10⁹⁷(98-digit number)
20949428836930018630…18361163743782010879
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 281090

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 d41e24a535afa740bc691d2584b1fa665202e7b470a4165664bdaaa9f22ced71

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 #281,090 on Chainz β†—
Circulating Supply:57,682,377 XPMΒ·at block #6,804,788 Β· updates every 60s
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