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Home/Chain Registry/Block #2,110,010

Block #2,110,010

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2017, 12:25:04 PM Β· Difficulty 10.9018 Β· 4,727,029 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd32a46fb793bb5cea73d70a1c78c0fac0b32d9fd399ad450ffe65337be68b82
View on Chainz β†—

Difficulty

10.901800

Transactions

1

Size

201 B

Version

2

Bits

0ae6dc57

Nonce

818,925,166

Timestamp

5/10/2017, 12:25:04 PM

Confirmations

4,727,029

Merkle Root

ac412ae382f6b6356abdfb9fb90d8b5e3e28cd7c5e7aa13936dfd0f1319672f5
Transactions (1)
Coinbaseac412ae382f6b6…dfd0f1319672f5
1 in β†’ 1 out8.4000 XPM110 B
AVAnPyUT…1BbHhHzW
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.

9.174 Γ— 10⁹⁡(96-digit number)
91743317957208423375…96145963090342763200
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
9.174 Γ— 10⁹⁡(96-digit number)
91743317957208423375…96145963090342763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁢(97-digit number)
18348663591441684675…92291926180685526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.669 Γ— 10⁹⁢(97-digit number)
36697327182883369350…84583852361371052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.339 Γ— 10⁹⁢(97-digit number)
73394654365766738700…69167704722742105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.467 Γ— 10⁹⁷(98-digit number)
14678930873153347740…38335409445484211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.935 Γ— 10⁹⁷(98-digit number)
29357861746306695480…76670818890968422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.871 Γ— 10⁹⁷(98-digit number)
58715723492613390960…53341637781936844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁸(99-digit number)
11743144698522678192…06683275563873689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.348 Γ— 10⁹⁸(99-digit number)
23486289397045356384…13366551127747379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.697 Γ— 10⁹⁸(99-digit number)
46972578794090712768…26733102255494758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.394 Γ— 10⁹⁸(99-digit number)
93945157588181425536…53466204510989516799
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 2110010

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 cd32a46fb793bb5cea73d70a1c78c0fac0b32d9fd399ad450ffe65337be68b82

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 #2,110,010 on Chainz β†—
Circulating Supply:57,940,614 XPMΒ·at block #6,837,038 Β· updates every 60s
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