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Home/Chain Registry/Block #3,016,782

Block #3,016,782

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2019, 9:15:01 PM Β· Difficulty 11.1678 Β· 3,828,110 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
434cec7fe7c20559902779cd4957b940063f6b8cdcbce9547afd80fe3ccf3a75
View on Chainz β†—

Difficulty

11.167785

Transactions

1

Size

201 B

Version

2

Bits

0b2af3fa

Nonce

1,259,098,753

Timestamp

1/19/2019, 9:15:01 PM

Confirmations

3,828,110

Merkle Root

355fb7866d1ca541e4834b8f4f0f4593046e6b8f9e683ece38daba8c2faf0ed6
Transactions (1)
Coinbase355fb7866d1ca5…daba8c2faf0ed6
1 in β†’ 1 out8.0000 XPM110 B
AUhjokok…k5m93PZR
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.

1.572 Γ— 10⁹⁢(97-digit number)
15723804860778446504…85796205759996672000
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
1.572 Γ— 10⁹⁢(97-digit number)
15723804860778446504…85796205759996671999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.572 Γ— 10⁹⁢(97-digit number)
15723804860778446504…85796205759996672001
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
3.144 Γ— 10⁹⁢(97-digit number)
31447609721556893008…71592411519993343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.144 Γ— 10⁹⁢(97-digit number)
31447609721556893008…71592411519993344001
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
6.289 Γ— 10⁹⁢(97-digit number)
62895219443113786017…43184823039986687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.289 Γ— 10⁹⁢(97-digit number)
62895219443113786017…43184823039986688001
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
1.257 Γ— 10⁹⁷(98-digit number)
12579043888622757203…86369646079973375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.257 Γ— 10⁹⁷(98-digit number)
12579043888622757203…86369646079973376001
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
2.515 Γ— 10⁹⁷(98-digit number)
25158087777245514407…72739292159946751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.515 Γ— 10⁹⁷(98-digit number)
25158087777245514407…72739292159946752001
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
5.031 Γ— 10⁹⁷(98-digit number)
50316175554491028814…45478584319893503999
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 3016782

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 434cec7fe7c20559902779cd4957b940063f6b8cdcbce9547afd80fe3ccf3a75

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 #3,016,782 on Chainz β†—
Circulating Supply:58,003,551 XPMΒ·at block #6,844,891 Β· updates every 60s
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