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Home/Chain Registry/Block #2,750,450

Block #2,750,450

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2018, 8:47:16 PM Β· Difficulty 11.6451 Β· 4,083,325 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
358fc3d16fb85356c9d5d7d83377890bb623b7fae7fb350acd5a7ba8890d3b48
View on Chainz β†—

Difficulty

11.645068

Transactions

2

Size

1020 B

Version

2

Bits

0ba52332

Nonce

524,241,062

Timestamp

7/15/2018, 8:47:16 PM

Confirmations

4,083,325

Merkle Root

4870428135a70df334bc837ef12accd4df905234bfcd7d96f8814a2ce5338337
Transactions (2)
Coinbase63863af841c8d3…411db5b5af7ab7
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
cf7ee423fa387e…f52936055ab5ef
5 in β†’ 2 out145.0100 XPM820 B
ASgQAKaS…aUdijMAFALucWQvB…Nj3CnX3n
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.

8.588 Γ— 10⁹⁴(95-digit number)
85887931011298919123…40347365848645301460
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
8.588 Γ— 10⁹⁴(95-digit number)
85887931011298919123…40347365848645301459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.717 Γ— 10⁹⁡(96-digit number)
17177586202259783824…80694731697290602919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.435 Γ— 10⁹⁡(96-digit number)
34355172404519567649…61389463394581205839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.871 Γ— 10⁹⁡(96-digit number)
68710344809039135298…22778926789162411679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.374 Γ— 10⁹⁢(97-digit number)
13742068961807827059…45557853578324823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.748 Γ— 10⁹⁢(97-digit number)
27484137923615654119…91115707156649646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.496 Γ— 10⁹⁢(97-digit number)
54968275847231308239…82231414313299293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁷(98-digit number)
10993655169446261647…64462828626598586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.198 Γ— 10⁹⁷(98-digit number)
21987310338892523295…28925657253197173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.397 Γ— 10⁹⁷(98-digit number)
43974620677785046591…57851314506394347519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.794 Γ— 10⁹⁷(98-digit number)
87949241355570093182…15702629012788695039
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 2750450

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 358fc3d16fb85356c9d5d7d83377890bb623b7fae7fb350acd5a7ba8890d3b48

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 #2,750,450 on Chainz β†—
Circulating Supply:57,914,418 XPMΒ·at block #6,833,774 Β· updates every 60s
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