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Home/Chain Registry/Block #2,807,259

Block #2,807,259

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/24/2018, 1:16:26 AM Β· Difficulty 11.6730 Β· 4,037,994 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc04ec463b788a3738073cdbf3cc52bf9faba83bc8d6619c7c2398a232681e9b
View on Chainz β†—

Difficulty

11.672953

Transactions

1

Size

200 B

Version

2

Bits

0bac46a9

Nonce

1,369,700,672

Timestamp

8/24/2018, 1:16:26 AM

Confirmations

4,037,994

Merkle Root

869cf743b6752261503540c2cb6ec2848c1fe660d3f0565df97b640969e3d0f7
Transactions (1)
Coinbase869cf743b67522…7b640969e3d0f7
1 in β†’ 1 out7.3300 XPM110 B
Aah7hxJK…RmHn6JrV
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.

7.524 Γ— 10⁹³(94-digit number)
75243647497282371249…13751094560993351660
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
7.524 Γ— 10⁹³(94-digit number)
75243647497282371249…13751094560993351659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁴(95-digit number)
15048729499456474249…27502189121986703319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.009 Γ— 10⁹⁴(95-digit number)
30097458998912948499…55004378243973406639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.019 Γ— 10⁹⁴(95-digit number)
60194917997825896999…10008756487946813279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁡(96-digit number)
12038983599565179399…20017512975893626559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.407 Γ— 10⁹⁡(96-digit number)
24077967199130358799…40035025951787253119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.815 Γ— 10⁹⁡(96-digit number)
48155934398260717599…80070051903574506239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.631 Γ— 10⁹⁡(96-digit number)
96311868796521435198…60140103807149012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.926 Γ— 10⁹⁢(97-digit number)
19262373759304287039…20280207614298024959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.852 Γ— 10⁹⁢(97-digit number)
38524747518608574079…40560415228596049919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.704 Γ— 10⁹⁢(97-digit number)
77049495037217148159…81120830457192099839
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 2807259

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 fc04ec463b788a3738073cdbf3cc52bf9faba83bc8d6619c7c2398a232681e9b

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 #2,807,259 on Chainz β†—
Circulating Supply:58,006,459 XPMΒ·at block #6,845,252 Β· updates every 60s
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