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Home/Chain Registry/Block #2,658,112

Block #2,658,112

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/12/2018, 2:11:39 PM Β· Difficulty 11.6570 Β· 4,184,422 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
08201fed0a5dfa9602cbd4b204ec0205dfda4cef6e91b86048884d1cfbd59979
View on Chainz β†—

Difficulty

11.656981

Transactions

1

Size

200 B

Version

2

Bits

0ba82fe5

Nonce

2,145,433,907

Timestamp

5/12/2018, 2:11:39 PM

Confirmations

4,184,422

Merkle Root

359d9fc63f257070dc8f4ca6a2aa4b3040756e64083f6a84d2a93ff67a011458
Transactions (1)
Coinbase359d9fc63f2570…a93ff67a011458
1 in β†’ 1 out7.3500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.758 Γ— 10⁹⁡(96-digit number)
17581721869374691523…10031293488793833600
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
1.758 Γ— 10⁹⁡(96-digit number)
17581721869374691523…10031293488793833599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.516 Γ— 10⁹⁡(96-digit number)
35163443738749383046…20062586977587667199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.032 Γ— 10⁹⁡(96-digit number)
70326887477498766093…40125173955175334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.406 Γ— 10⁹⁢(97-digit number)
14065377495499753218…80250347910350668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.813 Γ— 10⁹⁢(97-digit number)
28130754990999506437…60500695820701337599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.626 Γ— 10⁹⁢(97-digit number)
56261509981999012874…21001391641402675199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁷(98-digit number)
11252301996399802574…42002783282805350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.250 Γ— 10⁹⁷(98-digit number)
22504603992799605149…84005566565610700799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.500 Γ— 10⁹⁷(98-digit number)
45009207985599210299…68011133131221401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.001 Γ— 10⁹⁷(98-digit number)
90018415971198420599…36022266262442803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.800 Γ— 10⁹⁸(99-digit number)
18003683194239684119…72044532524885606399
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 2658112

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 08201fed0a5dfa9602cbd4b204ec0205dfda4cef6e91b86048884d1cfbd59979

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 #2,658,112 on Chainz β†—
Circulating Supply:57,984,694 XPMΒ·at block #6,842,533 Β· updates every 60s
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