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Home/Chain Registry/Block #2,128,792

Block #2,128,792

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/23/2017, 4:05:31 AM Β· Difficulty 10.9127 Β· 4,696,488 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca8ba8a779e7a3b9052b86ebd4f2f9bf147271e5ec83a4e0073e96667f478a82
View on Chainz β†—

Difficulty

10.912703

Transactions

1

Size

199 B

Version

2

Bits

0ae9a6e3

Nonce

2,055,444,047

Timestamp

5/23/2017, 4:05:31 AM

Confirmations

4,696,488

Merkle Root

982a1849c21656809567bbb7ee2672d3db0836210afe496ed51b27b718dd5620
Transactions (1)
Coinbase982a1849c21656…1b27b718dd5620
1 in β†’ 1 out8.3800 XPM109 B
ALMmUTqZ…pSv5kNzd
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.

3.695 Γ— 10⁹⁴(95-digit number)
36957298143253036925…52545399531463659520
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
3.695 Γ— 10⁹⁴(95-digit number)
36957298143253036925…52545399531463659519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.391 Γ— 10⁹⁴(95-digit number)
73914596286506073850…05090799062927319039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.478 Γ— 10⁹⁡(96-digit number)
14782919257301214770…10181598125854638079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.956 Γ— 10⁹⁡(96-digit number)
29565838514602429540…20363196251709276159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.913 Γ— 10⁹⁡(96-digit number)
59131677029204859080…40726392503418552319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁢(97-digit number)
11826335405840971816…81452785006837104639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.365 Γ— 10⁹⁢(97-digit number)
23652670811681943632…62905570013674209279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.730 Γ— 10⁹⁢(97-digit number)
47305341623363887264…25811140027348418559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.461 Γ— 10⁹⁢(97-digit number)
94610683246727774529…51622280054696837119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.892 Γ— 10⁹⁷(98-digit number)
18922136649345554905…03244560109393674239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2128792

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 ca8ba8a779e7a3b9052b86ebd4f2f9bf147271e5ec83a4e0073e96667f478a82

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 #2,128,792 on Chainz β†—
Circulating Supply:57,846,338 XPMΒ·at block #6,825,279 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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