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Home/Chain Registry/Block #2,828,546

Block #2,828,546

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2018, 9:37:48 AM Β· Difficulty 11.7117 Β· 4,014,592 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f6f70c3375da8999bfeb3173a2c2afb1f1632945ff595ca0e076b1efe888022b
View on Chainz β†—

Difficulty

11.711676

Transactions

1

Size

201 B

Version

2

Bits

0bb63069

Nonce

1,873,256,597

Timestamp

9/7/2018, 9:37:48 AM

Confirmations

4,014,592

Merkle Root

7ba145ef6793df049f8e93cfebea9acdfdbf854eb098694966545396c1e03bc8
Transactions (1)
Coinbase7ba145ef6793df…545396c1e03bc8
1 in β†’ 1 out7.2800 XPM111 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.

4.416 Γ— 10⁹³(94-digit number)
44162056444835795701…24516774769734350260
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
4.416 Γ— 10⁹³(94-digit number)
44162056444835795701…24516774769734350259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.416 Γ— 10⁹³(94-digit number)
44162056444835795701…24516774769734350261
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
8.832 Γ— 10⁹³(94-digit number)
88324112889671591403…49033549539468700519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.832 Γ— 10⁹³(94-digit number)
88324112889671591403…49033549539468700521
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
1.766 Γ— 10⁹⁴(95-digit number)
17664822577934318280…98067099078937401039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.766 Γ— 10⁹⁴(95-digit number)
17664822577934318280…98067099078937401041
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
3.532 Γ— 10⁹⁴(95-digit number)
35329645155868636561…96134198157874802079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.532 Γ— 10⁹⁴(95-digit number)
35329645155868636561…96134198157874802081
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
7.065 Γ— 10⁹⁴(95-digit number)
70659290311737273122…92268396315749604159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.065 Γ— 10⁹⁴(95-digit number)
70659290311737273122…92268396315749604161
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
1.413 Γ— 10⁹⁡(96-digit number)
14131858062347454624…84536792631499208319
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 2828546

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 f6f70c3375da8999bfeb3173a2c2afb1f1632945ff595ca0e076b1efe888022b

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 #2,828,546 on Chainz β†—
Circulating Supply:57,989,467 XPMΒ·at block #6,843,137 Β· updates every 60s
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