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Home/Chain Registry/Block #3,085,464

Block #3,085,464

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/9/2019, 1:43:54 PM Β· Difficulty 11.0311 Β· 3,758,410 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f46e61451043308855216bfb71cc66f9c3cf389336678bb4fb4243617d3bdc8
View on Chainz β†—

Difficulty

11.031123

Transactions

1

Size

200 B

Version

2

Bits

0b07f7b3

Nonce

1,632,287,688

Timestamp

3/9/2019, 1:43:54 PM

Confirmations

3,758,410

Merkle Root

50a357fa4ae95ae855a8674e96273774da3661e17786000adc57f32859d3b6a1
Transactions (1)
Coinbase50a357fa4ae95a…57f32859d3b6a1
1 in β†’ 1 out8.2000 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.

8.719 Γ— 10⁹⁴(95-digit number)
87193031377352756385…61854702052048880000
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
8.719 Γ— 10⁹⁴(95-digit number)
87193031377352756385…61854702052048879999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.719 Γ— 10⁹⁴(95-digit number)
87193031377352756385…61854702052048880001
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
1.743 Γ— 10⁹⁡(96-digit number)
17438606275470551277…23709404104097759999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.743 Γ— 10⁹⁡(96-digit number)
17438606275470551277…23709404104097760001
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
3.487 Γ— 10⁹⁡(96-digit number)
34877212550941102554…47418808208195519999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.487 Γ— 10⁹⁡(96-digit number)
34877212550941102554…47418808208195520001
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
6.975 Γ— 10⁹⁡(96-digit number)
69754425101882205108…94837616416391039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.975 Γ— 10⁹⁡(96-digit number)
69754425101882205108…94837616416391040001
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
1.395 Γ— 10⁹⁢(97-digit number)
13950885020376441021…89675232832782079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.395 Γ— 10⁹⁢(97-digit number)
13950885020376441021…89675232832782080001
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
2.790 Γ— 10⁹⁢(97-digit number)
27901770040752882043…79350465665564159999
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 3085464

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 0f46e61451043308855216bfb71cc66f9c3cf389336678bb4fb4243617d3bdc8

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 #3,085,464 on Chainz β†—
Circulating Supply:57,995,362 XPMΒ·at block #6,843,873 Β· updates every 60s
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