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Home/Chain Registry/Block #2,924,827

Block #2,924,827

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 2:27:54 AM Β· Difficulty 11.3573 Β· 3,917,517 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ba33505a1c128f0c211db3025e896e2e97f05232a675f76203e041dcd586c98
View on Chainz β†—

Difficulty

11.357298

Transactions

1

Size

200 B

Version

2

Bits

0b5b77df

Nonce

1,878,394,126

Timestamp

11/16/2018, 2:27:54 AM

Confirmations

3,917,517

Merkle Root

7cd9ce7d98c8682167e60b5ba8d964a63b7410df2db29fbf79965bd85e73bf68
Transactions (1)
Coinbase7cd9ce7d98c868…965bd85e73bf68
1 in β†’ 1 out7.7400 XPM110 B
AbXwmGxD…4XXYP765
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.

2.686 Γ— 10⁹⁡(96-digit number)
26866938983843446055…40927955176457831040
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
2.686 Γ— 10⁹⁡(96-digit number)
26866938983843446055…40927955176457831039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.373 Γ— 10⁹⁡(96-digit number)
53733877967686892110…81855910352915662079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁢(97-digit number)
10746775593537378422…63711820705831324159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁢(97-digit number)
21493551187074756844…27423641411662648319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.298 Γ— 10⁹⁢(97-digit number)
42987102374149513688…54847282823325296639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.597 Γ— 10⁹⁢(97-digit number)
85974204748299027377…09694565646650593279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁷(98-digit number)
17194840949659805475…19389131293301186559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.438 Γ— 10⁹⁷(98-digit number)
34389681899319610950…38778262586602373119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.877 Γ— 10⁹⁷(98-digit number)
68779363798639221901…77556525173204746239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.375 Γ— 10⁹⁸(99-digit number)
13755872759727844380…55113050346409492479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.751 Γ— 10⁹⁸(99-digit number)
27511745519455688760…10226100692818984959
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 2924827

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 9ba33505a1c128f0c211db3025e896e2e97f05232a675f76203e041dcd586c98

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 #2,924,827 on Chainz β†—
Circulating Supply:57,983,159 XPMΒ·at block #6,842,343 Β· updates every 60s
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