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Home/Chain Registry/Block #3,077,068

Block #3,077,068

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/3/2019, 7:53:30 PM Β· Difficulty 11.0064 Β· 3,766,850 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb152ced10fdd0c3200e508e60e6b1767fcaf122298bf2d6c796962dec947b2f
View on Chainz β†—

Difficulty

11.006386

Transactions

1

Size

200 B

Version

2

Bits

0b01a28b

Nonce

1,080,281,212

Timestamp

3/3/2019, 7:53:30 PM

Confirmations

3,766,850

Merkle Root

33e7206122607e32c0b262f2c0ae119ab65a56900b2e9e6fbb4f80ff8c7f1714
Transactions (1)
Coinbase33e7206122607e…4f80ff8c7f1714
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.

7.740 Γ— 10⁹⁡(96-digit number)
77406732307529241584…80917014003959380480
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
7.740 Γ— 10⁹⁡(96-digit number)
77406732307529241584…80917014003959380479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.740 Γ— 10⁹⁡(96-digit number)
77406732307529241584…80917014003959380481
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
1.548 Γ— 10⁹⁢(97-digit number)
15481346461505848316…61834028007918760959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15481346461505848316…61834028007918760961
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
3.096 Γ— 10⁹⁢(97-digit number)
30962692923011696633…23668056015837521919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.096 Γ— 10⁹⁢(97-digit number)
30962692923011696633…23668056015837521921
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
6.192 Γ— 10⁹⁢(97-digit number)
61925385846023393267…47336112031675043839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.192 Γ— 10⁹⁢(97-digit number)
61925385846023393267…47336112031675043841
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
1.238 Γ— 10⁹⁷(98-digit number)
12385077169204678653…94672224063350087679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.238 Γ— 10⁹⁷(98-digit number)
12385077169204678653…94672224063350087681
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
2.477 Γ— 10⁹⁷(98-digit number)
24770154338409357307…89344448126700175359
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 3077068

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 fb152ced10fdd0c3200e508e60e6b1767fcaf122298bf2d6c796962dec947b2f

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 #3,077,068 on Chainz β†—
Circulating Supply:57,995,715 XPMΒ·at block #6,843,917 Β· updates every 60s
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