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Home/Chain Registry/Block #2,300,062

Block #2,300,062

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2017, 9:30:28 AM Β· Difficulty 10.9348 Β· 4,538,800 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
764626362dc6c9ba7d2eecb9c07a6bc4e4757d553fc644498be6a5ca9c24fceb
View on Chainz β†—

Difficulty

10.934816

Transactions

1

Size

200 B

Version

2

Bits

0aef5022

Nonce

860,701,383

Timestamp

9/18/2017, 9:30:28 AM

Confirmations

4,538,800

Merkle Root

2bf159489d090039b50634a1ad4d4ef63cba7ecd4fdd9dc649461017d52f0a32
Transactions (1)
Coinbase2bf159489d0900…461017d52f0a32
1 in β†’ 1 out8.3500 XPM110 B
AHfGXPm4…RxZcfV39
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.

6.700 Γ— 10⁹⁴(95-digit number)
67000318112906950120…78256764460185933800
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
6.700 Γ— 10⁹⁴(95-digit number)
67000318112906950120…78256764460185933801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.340 Γ— 10⁹⁡(96-digit number)
13400063622581390024…56513528920371867601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.680 Γ— 10⁹⁡(96-digit number)
26800127245162780048…13027057840743735201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.360 Γ— 10⁹⁡(96-digit number)
53600254490325560096…26054115681487470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.072 Γ— 10⁹⁢(97-digit number)
10720050898065112019…52108231362974940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.144 Γ— 10⁹⁢(97-digit number)
21440101796130224038…04216462725949881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.288 Γ— 10⁹⁢(97-digit number)
42880203592260448077…08432925451899763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.576 Γ— 10⁹⁢(97-digit number)
85760407184520896154…16865850903799526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.715 Γ— 10⁹⁷(98-digit number)
17152081436904179230…33731701807599052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.430 Γ— 10⁹⁷(98-digit number)
34304162873808358461…67463403615198105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.860 Γ— 10⁹⁷(98-digit number)
68608325747616716923…34926807230396211201
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 2300062

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 764626362dc6c9ba7d2eecb9c07a6bc4e4757d553fc644498be6a5ca9c24fceb

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 #2,300,062 on Chainz β†—
Circulating Supply:57,955,161 XPMΒ·at block #6,838,861 Β· updates every 60s
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