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Home/Chain Registry/Block #2,110,045

Block #2,110,045

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2017, 12:49:05 PM Β· Difficulty 10.9020 Β· 4,732,061 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b43f72c41f7dd1016ba816191db629ab43b7f206e5f345d8165a6c495d819fe8
View on Chainz β†—

Difficulty

10.901975

Transactions

1

Size

201 B

Version

2

Bits

0ae6e7dd

Nonce

1,370,077,808

Timestamp

5/10/2017, 12:49:05 PM

Confirmations

4,732,061

Merkle Root

7f3c0e2de86ae1d4cf0285536a5d5a5954a4260d4f11ab5e9d4279f5adf96dd8
Transactions (1)
Coinbase7f3c0e2de86ae1…4279f5adf96dd8
1 in β†’ 1 out8.4000 XPM110 B
Ac7DPpKR…u7hHgFVJ
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.

1.302 Γ— 10⁹⁢(97-digit number)
13029595945476949920…93503257218389766400
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
1.302 Γ— 10⁹⁢(97-digit number)
13029595945476949920…93503257218389766399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.605 Γ— 10⁹⁢(97-digit number)
26059191890953899841…87006514436779532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.211 Γ— 10⁹⁢(97-digit number)
52118383781907799683…74013028873559065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.042 Γ— 10⁹⁷(98-digit number)
10423676756381559936…48026057747118131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.084 Γ— 10⁹⁷(98-digit number)
20847353512763119873…96052115494236262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.169 Γ— 10⁹⁷(98-digit number)
41694707025526239746…92104230988472524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.338 Γ— 10⁹⁷(98-digit number)
83389414051052479492…84208461976945049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.667 Γ— 10⁹⁸(99-digit number)
16677882810210495898…68416923953890099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.335 Γ— 10⁹⁸(99-digit number)
33355765620420991797…36833847907780198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.671 Γ— 10⁹⁸(99-digit number)
66711531240841983594…73667695815560396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁹(100-digit number)
13342306248168396718…47335391631120793599
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 2110045

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 b43f72c41f7dd1016ba816191db629ab43b7f206e5f345d8165a6c495d819fe8

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 #2,110,045 on Chainz β†—
Circulating Supply:57,981,235 XPMΒ·at block #6,842,105 Β· updates every 60s
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