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Home/Chain Registry/Block #2,925,249

Block #2,925,249

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 9:49:46 AM Β· Difficulty 11.3548 Β· 3,906,332 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c88278192636221b55da1517deac56366d640fabfbbf020aee969638c4639ad3
View on Chainz β†—

Difficulty

11.354803

Transactions

1

Size

200 B

Version

2

Bits

0b5ad459

Nonce

562,136,560

Timestamp

11/16/2018, 9:49:46 AM

Confirmations

3,906,332

Merkle Root

630871f4cc025947a04474698b82749eede41de2b8018129700d8cff4ad7be13
Transactions (1)
Coinbase630871f4cc0259…0d8cff4ad7be13
1 in β†’ 1 out7.7400 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.946 Γ— 10⁹⁴(95-digit number)
19460838439769672656…73716478712142629120
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
1.946 Γ— 10⁹⁴(95-digit number)
19460838439769672656…73716478712142629121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.892 Γ— 10⁹⁴(95-digit number)
38921676879539345313…47432957424285258241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.784 Γ— 10⁹⁴(95-digit number)
77843353759078690627…94865914848570516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.556 Γ— 10⁹⁡(96-digit number)
15568670751815738125…89731829697141032961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.113 Γ— 10⁹⁡(96-digit number)
31137341503631476250…79463659394282065921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.227 Γ— 10⁹⁡(96-digit number)
62274683007262952501…58927318788564131841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.245 Γ— 10⁹⁢(97-digit number)
12454936601452590500…17854637577128263681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.490 Γ— 10⁹⁢(97-digit number)
24909873202905181000…35709275154256527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.981 Γ— 10⁹⁢(97-digit number)
49819746405810362001…71418550308513054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.963 Γ— 10⁹⁢(97-digit number)
99639492811620724002…42837100617026109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.992 Γ— 10⁹⁷(98-digit number)
19927898562324144800…85674201234052218881
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 2925249

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 c88278192636221b55da1517deac56366d640fabfbbf020aee969638c4639ad3

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 #2,925,249 on Chainz β†—
Circulating Supply:57,896,743 XPMΒ·at block #6,831,580 Β· updates every 60s
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