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Home/Chain Registry/Block #2,642,065

Block #2,642,065

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 2:25:41 PM Β· Difficulty 11.6408 Β· 4,188,940 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9625fc0a19e14d7dca7cb0bb717b6c414c16dd3b55e780a8f95f04bd01653004
View on Chainz β†—

Difficulty

11.640826

Transactions

1

Size

199 B

Version

2

Bits

0ba40d2e

Nonce

1,821,781,015

Timestamp

5/1/2018, 2:25:41 PM

Confirmations

4,188,940

Merkle Root

fafd8a349e45c1e6b7cac15abcebacba8505e1e068a24165386e1c8182aff149
Transactions (1)
Coinbasefafd8a349e45c1…6e1c8182aff149
1 in β†’ 1 out7.3700 XPM110 B
AU7aU96C…G5daTAMw
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.

1.185 Γ— 10⁹²(93-digit number)
11853522865623064476…43804782991227332360
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
1.185 Γ— 10⁹²(93-digit number)
11853522865623064476…43804782991227332359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.370 Γ— 10⁹²(93-digit number)
23707045731246128953…87609565982454664719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.741 Γ— 10⁹²(93-digit number)
47414091462492257906…75219131964909329439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.482 Γ— 10⁹²(93-digit number)
94828182924984515812…50438263929818658879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.896 Γ— 10⁹³(94-digit number)
18965636584996903162…00876527859637317759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.793 Γ— 10⁹³(94-digit number)
37931273169993806324…01753055719274635519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.586 Γ— 10⁹³(94-digit number)
75862546339987612649…03506111438549271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁴(95-digit number)
15172509267997522529…07012222877098542079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.034 Γ— 10⁹⁴(95-digit number)
30345018535995045059…14024445754197084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.069 Γ— 10⁹⁴(95-digit number)
60690037071990090119…28048891508394168319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁡(96-digit number)
12138007414398018023…56097783016788336639
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 2642065

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 9625fc0a19e14d7dca7cb0bb717b6c414c16dd3b55e780a8f95f04bd01653004

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 #2,642,065 on Chainz β†—
Circulating Supply:57,892,181 XPMΒ·at block #6,831,004 Β· updates every 60s
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