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Home/Chain Registry/Block #2,825,869

Block #2,825,869

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2018, 1:25:39 PM Β· Difficulty 11.7101 Β· 4,017,936 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
1c73b6f8cc2cb3e6607d70287b6683ae89342fa0b02a3db8b1e59f1204c7b140
View on Chainz β†—

Difficulty

11.710140

Transactions

1

Size

200 B

Version

2

Bits

0bb5cbb5

Nonce

568,934,709

Timestamp

9/5/2018, 1:25:39 PM

Confirmations

4,017,936

Merkle Root

cc3c64353257f127d8ebb1bdc8500eaff220e64b435ec6a188f91d3129080405
Transactions (1)
Coinbasecc3c64353257f1…f91d3129080405
1 in β†’ 1 out7.2800 XPM110 B
AH7v8zn5…7GkMq4JB
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.

9.073 Γ— 10⁹³(94-digit number)
90732030630740577037…52119239237996626990
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
9.073 Γ— 10⁹³(94-digit number)
90732030630740577037…52119239237996626989
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.073 Γ— 10⁹³(94-digit number)
90732030630740577037…52119239237996626991
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.814 Γ— 10⁹⁴(95-digit number)
18146406126148115407…04238478475993253979
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.814 Γ— 10⁹⁴(95-digit number)
18146406126148115407…04238478475993253981
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.629 Γ— 10⁹⁴(95-digit number)
36292812252296230814…08476956951986507959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.629 Γ— 10⁹⁴(95-digit number)
36292812252296230814…08476956951986507961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
7.258 Γ— 10⁹⁴(95-digit number)
72585624504592461629…16953913903973015919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.258 Γ— 10⁹⁴(95-digit number)
72585624504592461629…16953913903973015921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.451 Γ— 10⁹⁡(96-digit number)
14517124900918492325…33907827807946031839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.451 Γ— 10⁹⁡(96-digit number)
14517124900918492325…33907827807946031841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.903 Γ— 10⁹⁡(96-digit number)
29034249801836984651…67815655615892063679
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 2825869

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 1c73b6f8cc2cb3e6607d70287b6683ae89342fa0b02a3db8b1e59f1204c7b140

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 #2,825,869 on Chainz β†—
Circulating Supply:57,994,814 XPMΒ·at block #6,843,804 Β· updates every 60s
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