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Home/Chain Registry/Block #2,825,826

Block #2,825,826

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2018, 12:44:10 PM Β· Difficulty 11.7101 Β· 4,017,902 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be4b27449e50295741c831f37dbfc9a26db6ea95185f50c0de5feb74c8702cae
View on Chainz β†—

Difficulty

11.710108

Transactions

1

Size

202 B

Version

2

Bits

0bb5c9ab

Nonce

163,682,943

Timestamp

9/5/2018, 12:44:10 PM

Confirmations

4,017,902

Merkle Root

a9223213a86930788cfa926bf2f9931bcd368fecaa3db1a6cdb6179fae8d60a4
Transactions (1)
Coinbasea9223213a86930…b6179fae8d60a4
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.526 Γ— 10⁹⁹(100-digit number)
25266715969635822930…55659014971397570560
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
2.526 Γ— 10⁹⁹(100-digit number)
25266715969635822930…55659014971397570559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.526 Γ— 10⁹⁹(100-digit number)
25266715969635822930…55659014971397570561
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
5.053 Γ— 10⁹⁹(100-digit number)
50533431939271645861…11318029942795141119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.053 Γ— 10⁹⁹(100-digit number)
50533431939271645861…11318029942795141121
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
1.010 Γ— 10¹⁰⁰(101-digit number)
10106686387854329172…22636059885590282239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.010 Γ— 10¹⁰⁰(101-digit number)
10106686387854329172…22636059885590282241
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
2.021 Γ— 10¹⁰⁰(101-digit number)
20213372775708658344…45272119771180564479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.021 Γ— 10¹⁰⁰(101-digit number)
20213372775708658344…45272119771180564481
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
4.042 Γ— 10¹⁰⁰(101-digit number)
40426745551417316689…90544239542361128959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.042 Γ— 10¹⁰⁰(101-digit number)
40426745551417316689…90544239542361128961
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
8.085 Γ— 10¹⁰⁰(101-digit number)
80853491102834633379…81088479084722257919
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 2825826

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 be4b27449e50295741c831f37dbfc9a26db6ea95185f50c0de5feb74c8702cae

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 #2,825,826 on Chainz β†—
Circulating Supply:57,994,195 XPMΒ·at block #6,843,727 Β· updates every 60s
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