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Home/Chain Registry/Block #2,924,816

Block #2,924,816

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 2:17:49 AM Β· Difficulty 11.3572 Β· 3,916,393 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fbb2af0e47aaf0fa38fac0d9e8e76ac4b052d586442cb5fdf1547978f9fba1c1
View on Chainz β†—

Difficulty

11.357202

Transactions

1

Size

200 B

Version

2

Bits

0b5b7194

Nonce

1,335,440,872

Timestamp

11/16/2018, 2:17:49 AM

Confirmations

3,916,393

Merkle Root

2c2172314ff10c0c0f888472c01210733ab61cb6c62dbab24150be5f98b251dc
Transactions (1)
Coinbase2c2172314ff10c…50be5f98b251dc
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.

4.033 Γ— 10⁹³(94-digit number)
40330240676261429023…26382781472082597000
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
4.033 Γ— 10⁹³(94-digit number)
40330240676261429023…26382781472082597001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.066 Γ— 10⁹³(94-digit number)
80660481352522858047…52765562944165194001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.613 Γ— 10⁹⁴(95-digit number)
16132096270504571609…05531125888330388001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.226 Γ— 10⁹⁴(95-digit number)
32264192541009143218…11062251776660776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.452 Γ— 10⁹⁴(95-digit number)
64528385082018286437…22124503553321552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.290 Γ— 10⁹⁡(96-digit number)
12905677016403657287…44249007106643104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.581 Γ— 10⁹⁡(96-digit number)
25811354032807314575…88498014213286208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.162 Γ— 10⁹⁡(96-digit number)
51622708065614629150…76996028426572416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.032 Γ— 10⁹⁢(97-digit number)
10324541613122925830…53992056853144832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.064 Γ— 10⁹⁢(97-digit number)
20649083226245851660…07984113706289664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.129 Γ— 10⁹⁢(97-digit number)
41298166452491703320…15968227412579328001
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 2924816

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 fbb2af0e47aaf0fa38fac0d9e8e76ac4b052d586442cb5fdf1547978f9fba1c1

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 #2,924,816 on Chainz β†—
Circulating Supply:57,974,035 XPMΒ·at block #6,841,208 Β· updates every 60s
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