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Home/Chain Registry/Block #2,815,539

Block #2,815,539

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2018, 4:28:16 PM Β· Difficulty 11.6838 Β· 4,024,377 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30ef7aabdbf9d3a1173a2a7f716e03c978308fc3eb29813bc7b8fd5c9843db80
View on Chainz β†—

Difficulty

11.683799

Transactions

1

Size

201 B

Version

2

Bits

0baf0d72

Nonce

573,361,906

Timestamp

8/29/2018, 4:28:16 PM

Confirmations

4,024,377

Merkle Root

eeb5a02be28258c9f6642e6b6af69bf9d86391df008f1ee9f6f8b19b900e4d5a
Transactions (1)
Coinbaseeeb5a02be28258…f8b19b900e4d5a
1 in β†’ 1 out7.3100 XPM109 B
AX1Miuux…G3DzsA7E
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.

4.403 Γ— 10⁹⁸(99-digit number)
44039172363070293970…17569581357622558720
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
4.403 Γ— 10⁹⁸(99-digit number)
44039172363070293970…17569581357622558719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.403 Γ— 10⁹⁸(99-digit number)
44039172363070293970…17569581357622558721
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
8.807 Γ— 10⁹⁸(99-digit number)
88078344726140587940…35139162715245117439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.807 Γ— 10⁹⁸(99-digit number)
88078344726140587940…35139162715245117441
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
1.761 Γ— 10⁹⁹(100-digit number)
17615668945228117588…70278325430490234879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.761 Γ— 10⁹⁹(100-digit number)
17615668945228117588…70278325430490234881
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
3.523 Γ— 10⁹⁹(100-digit number)
35231337890456235176…40556650860980469759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.523 Γ— 10⁹⁹(100-digit number)
35231337890456235176…40556650860980469761
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
7.046 Γ— 10⁹⁹(100-digit number)
70462675780912470352…81113301721960939519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.046 Γ— 10⁹⁹(100-digit number)
70462675780912470352…81113301721960939521
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
1.409 Γ— 10¹⁰⁰(101-digit number)
14092535156182494070…62226603443921879039
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 2815539

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 30ef7aabdbf9d3a1173a2a7f716e03c978308fc3eb29813bc7b8fd5c9843db80

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 #2,815,539 on Chainz β†—
Circulating Supply:57,963,628 XPMΒ·at block #6,839,915 Β· updates every 60s
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