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Home/Chain Registry/Block #2,601,724

Block #2,601,724

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/5/2018, 8:00:47 PM Β· Difficulty 11.3161 Β· 4,236,285 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c24e1c5b10420b01eca1c691db3189cf0d9f0e4b0cc490e216effb9b62e7bede
View on Chainz β†—

Difficulty

11.316130

Transactions

1

Size

201 B

Version

2

Bits

0b50ede8

Nonce

293,986,842

Timestamp

4/5/2018, 8:00:47 PM

Confirmations

4,236,285

Merkle Root

3a1fa1b2e08318a5149805805c0bb95be340c155823e002c6a2476e1c45e0c28
Transactions (1)
Coinbase3a1fa1b2e08318…2476e1c45e0c28
1 in β†’ 1 out7.8000 XPM110 B
AKrgeocG…CVtXWBV3
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.

1.692 Γ— 10⁹⁸(99-digit number)
16923948980266942665…66665960879043215360
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.692 Γ— 10⁹⁸(99-digit number)
16923948980266942665…66665960879043215361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.384 Γ— 10⁹⁸(99-digit number)
33847897960533885331…33331921758086430721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.769 Γ— 10⁹⁸(99-digit number)
67695795921067770663…66663843516172861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.353 Γ— 10⁹⁹(100-digit number)
13539159184213554132…33327687032345722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.707 Γ— 10⁹⁹(100-digit number)
27078318368427108265…66655374064691445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.415 Γ— 10⁹⁹(100-digit number)
54156636736854216531…33310748129382891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.083 Γ— 10¹⁰⁰(101-digit number)
10831327347370843306…66621496258765783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.166 Γ— 10¹⁰⁰(101-digit number)
21662654694741686612…33242992517531566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.332 Γ— 10¹⁰⁰(101-digit number)
43325309389483373224…66485985035063132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.665 Γ— 10¹⁰⁰(101-digit number)
86650618778966746449…32971970070126264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.733 Γ— 10¹⁰¹(102-digit number)
17330123755793349289…65943940140252528641
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2601724

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 c24e1c5b10420b01eca1c691db3189cf0d9f0e4b0cc490e216effb9b62e7bede

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 #2,601,724 on Chainz β†—
Circulating Supply:57,948,425 XPMΒ·at block #6,838,008 Β· updates every 60s
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