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Home/Chain Registry/Block #2,925,481

Block #2,925,481

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 1:49:37 PM Β· Difficulty 11.3539 Β· 3,912,968 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c22164e6baf0b8efa713759430f1e518c8bd48113f62534d7b5be30566214d38
View on Chainz β†—

Difficulty

11.353892

Transactions

1

Size

200 B

Version

2

Bits

0b5a98a6

Nonce

396,913,213

Timestamp

11/16/2018, 1:49:37 PM

Confirmations

3,912,968

Merkle Root

2affde772e300dfd3f711012000ffcfc8dbfcf5d626b6f934f94f4cc8864de29
Transactions (1)
Coinbase2affde772e300d…94f4cc8864de29
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.

3.804 Γ— 10⁹³(94-digit number)
38043441251091251780…67890179307716224120
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
3.804 Γ— 10⁹³(94-digit number)
38043441251091251780…67890179307716224119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.608 Γ— 10⁹³(94-digit number)
76086882502182503560…35780358615432448239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁴(95-digit number)
15217376500436500712…71560717230864896479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁴(95-digit number)
30434753000873001424…43121434461729792959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.086 Γ— 10⁹⁴(95-digit number)
60869506001746002848…86242868923459585919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁡(96-digit number)
12173901200349200569…72485737846919171839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.434 Γ— 10⁹⁡(96-digit number)
24347802400698401139…44971475693838343679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.869 Γ— 10⁹⁡(96-digit number)
48695604801396802278…89942951387676687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.739 Γ— 10⁹⁡(96-digit number)
97391209602793604557…79885902775353374719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁢(97-digit number)
19478241920558720911…59771805550706749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁢(97-digit number)
38956483841117441823…19543611101413498879
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 2925481

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 c22164e6baf0b8efa713759430f1e518c8bd48113f62534d7b5be30566214d38

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 #2,925,481 on Chainz β†—
Circulating Supply:57,951,868 XPMΒ·at block #6,838,448 Β· updates every 60s
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