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Home/Chain Registry/Block #3,062,925

Block #3,062,925

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/21/2019, 6:07:35 PM Β· Difficulty 11.0101 Β· 3,780,454 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ecbe6cce00ea455ab64bf165b0ccec5d94521c8836f871d42461b2e472d76c0
View on Chainz β†—

Difficulty

11.010056

Transactions

1

Size

199 B

Version

2

Bits

0b029307

Nonce

942,647,200

Timestamp

2/21/2019, 6:07:35 PM

Confirmations

3,780,454

Merkle Root

a2f36ff3eda2ca25bca5f7847e49bf45bcd83ca5849ba4cab0d256b75584e8f6
Transactions (1)
Coinbasea2f36ff3eda2ca…d256b75584e8f6
1 in β†’ 1 out8.2400 XPM109 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.

4.698 Γ— 10⁹⁴(95-digit number)
46980791792166291623…31072322240903479040
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
4.698 Γ— 10⁹⁴(95-digit number)
46980791792166291623…31072322240903479041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.396 Γ— 10⁹⁴(95-digit number)
93961583584332583246…62144644481806958081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.879 Γ— 10⁹⁡(96-digit number)
18792316716866516649…24289288963613916161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.758 Γ— 10⁹⁡(96-digit number)
37584633433733033298…48578577927227832321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.516 Γ— 10⁹⁡(96-digit number)
75169266867466066597…97157155854455664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.503 Γ— 10⁹⁢(97-digit number)
15033853373493213319…94314311708911329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.006 Γ— 10⁹⁢(97-digit number)
30067706746986426639…88628623417822658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.013 Γ— 10⁹⁢(97-digit number)
60135413493972853278…77257246835645317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.202 Γ— 10⁹⁷(98-digit number)
12027082698794570655…54514493671290634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.405 Γ— 10⁹⁷(98-digit number)
24054165397589141311…09028987342581268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.810 Γ— 10⁹⁷(98-digit number)
48108330795178282622…18057974685162536961
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 3062925

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 9ecbe6cce00ea455ab64bf165b0ccec5d94521c8836f871d42461b2e472d76c0

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 #3,062,925 on Chainz β†—
Circulating Supply:57,991,396 XPMΒ·at block #6,843,378 Β· updates every 60s
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