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Home/Chain Registry/Block #2,649,519

Block #2,649,519

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 7:28:00 AM Β· Difficulty 11.7640 Β· 4,183,950 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bdf4a25be0783e51f7fd24039f1cc63f904fc4396dd94ba2194e59d020071012
View on Chainz β†—

Difficulty

11.763984

Transactions

2

Size

428 B

Version

2

Bits

0bc39471

Nonce

1,995,077,295

Timestamp

5/5/2018, 7:28:00 AM

Confirmations

4,183,950

Merkle Root

4e47196de5d207b2ab56235de9c73b40a5636764c322b5a9f3b27b1b798ff852
Transactions (2)
Coinbase89624a0105de42…fe0bb40edce4d8
1 in β†’ 1 out7.2200 XPM110 B
AXsTVFBq…5XSfgZNY
a0f4d99d2a1171…83c40567c81da8
1 in β†’ 2 out1866.3025 XPM227 B
AGGn6SJu…QVxKbSrUALZ9p3Jj…Nc8qTRsf
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.

7.038 Γ— 10⁹⁢(97-digit number)
70386998727304205296…44565201424543866880
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
7.038 Γ— 10⁹⁢(97-digit number)
70386998727304205296…44565201424543866879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.038 Γ— 10⁹⁢(97-digit number)
70386998727304205296…44565201424543866881
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
1.407 Γ— 10⁹⁷(98-digit number)
14077399745460841059…89130402849087733759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.407 Γ— 10⁹⁷(98-digit number)
14077399745460841059…89130402849087733761
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
2.815 Γ— 10⁹⁷(98-digit number)
28154799490921682118…78260805698175467519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.815 Γ— 10⁹⁷(98-digit number)
28154799490921682118…78260805698175467521
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
5.630 Γ— 10⁹⁷(98-digit number)
56309598981843364237…56521611396350935039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.630 Γ— 10⁹⁷(98-digit number)
56309598981843364237…56521611396350935041
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
1.126 Γ— 10⁹⁸(99-digit number)
11261919796368672847…13043222792701870079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.126 Γ— 10⁹⁸(99-digit number)
11261919796368672847…13043222792701870081
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
2.252 Γ— 10⁹⁸(99-digit number)
22523839592737345694…26086445585403740159
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 2649519

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 bdf4a25be0783e51f7fd24039f1cc63f904fc4396dd94ba2194e59d020071012

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 #2,649,519 on Chainz β†—
Circulating Supply:57,911,953 XPMΒ·at block #6,833,468 Β· updates every 60s
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