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Home/Chain Registry/Block #2,825,872

Block #2,825,872

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2018, 1:26:58 PM Β· Difficulty 11.7103 Β· 4,019,776 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d538444e7ef44c526dc3227c348c2f2b44c56bafe664f132c91947892854be12
View on Chainz β†—

Difficulty

11.710272

Transactions

1

Size

200 B

Version

2

Bits

0bb5d461

Nonce

224,095,209

Timestamp

9/5/2018, 1:26:58 PM

Confirmations

4,019,776

Merkle Root

72c9a5e7cf0c9b1ea5772c02beaa8af53324a6b1d048860bb73efcbcc6863473
Transactions (1)
Coinbase72c9a5e7cf0c9b…3efcbcc6863473
1 in β†’ 1 out7.2800 XPM110 B
AR2mL62K…WDZVcFd1
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.

3.168 Γ— 10⁹⁴(95-digit number)
31680882537622642515…89227857960277089040
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
3.168 Γ— 10⁹⁴(95-digit number)
31680882537622642515…89227857960277089041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.336 Γ— 10⁹⁴(95-digit number)
63361765075245285030…78455715920554178081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.267 Γ— 10⁹⁡(96-digit number)
12672353015049057006…56911431841108356161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.534 Γ— 10⁹⁡(96-digit number)
25344706030098114012…13822863682216712321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.068 Γ— 10⁹⁡(96-digit number)
50689412060196228024…27645727364433424641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10137882412039245604…55291454728866849281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20275764824078491209…10582909457733698561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.055 Γ— 10⁹⁢(97-digit number)
40551529648156982419…21165818915467397121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.110 Γ— 10⁹⁢(97-digit number)
81103059296313964838…42331637830934794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.622 Γ— 10⁹⁷(98-digit number)
16220611859262792967…84663275661869588481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.244 Γ— 10⁹⁷(98-digit number)
32441223718525585935…69326551323739176961
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 2825872

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 d538444e7ef44c526dc3227c348c2f2b44c56bafe664f132c91947892854be12

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 #2,825,872 on Chainz β†—
Circulating Supply:58,009,633 XPMΒ·at block #6,845,647 Β· updates every 60s
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