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Block #2,293,488

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/12/2017, 2:04:36 PM Β· Difficulty 10.9541 Β· 4,539,023 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6804b580457c45911e68fdd7446516a558b7664a5d610ed40aad8135b6bcbe22
View on Chainz β†—

Difficulty

10.954133

Transactions

1

Size

199 B

Version

2

Bits

0af44208

Nonce

817,559,085

Timestamp

9/12/2017, 2:04:36 PM

Confirmations

4,539,023

Merkle Root

f4f2f709d03b91a442a506078aabd525ccff53891847cdcd677f32faf8ebb611
Transactions (1)
Coinbasef4f2f709d03b91…7f32faf8ebb611
1 in β†’ 1 out8.3200 XPM109 B
AQBFPWCx…DHgrt1xW
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.

7.136 Γ— 10⁹⁴(95-digit number)
71361105249367189714…85918773881058115840
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
7.136 Γ— 10⁹⁴(95-digit number)
71361105249367189714…85918773881058115839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁡(96-digit number)
14272221049873437942…71837547762116231679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.854 Γ— 10⁹⁡(96-digit number)
28544442099746875885…43675095524232463359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.708 Γ— 10⁹⁡(96-digit number)
57088884199493751771…87350191048464926719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁢(97-digit number)
11417776839898750354…74700382096929853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.283 Γ— 10⁹⁢(97-digit number)
22835553679797500708…49400764193859706879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.567 Γ— 10⁹⁢(97-digit number)
45671107359595001417…98801528387719413759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.134 Γ— 10⁹⁢(97-digit number)
91342214719190002835…97603056775438827519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁷(98-digit number)
18268442943838000567…95206113550877655039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.653 Γ— 10⁹⁷(98-digit number)
36536885887676001134…90412227101755310079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.307 Γ— 10⁹⁷(98-digit number)
73073771775352002268…80824454203510620159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2293488

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 6804b580457c45911e68fdd7446516a558b7664a5d610ed40aad8135b6bcbe22

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 #2,293,488 on Chainz β†—
Circulating Supply:57,904,245 XPMΒ·at block #6,832,510 Β· updates every 60s
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