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Home/Chain Registry/Block #2,165,383

Block #2,165,383

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2017, 3:38:59 AM Β· Difficulty 10.8984 Β· 4,660,758 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75313abbb41d19120b3a06e05da32a4c7e2ae9a16e8d6bf669d895a4b3b09285
View on Chainz β†—

Difficulty

10.898385

Transactions

2

Size

426 B

Version

2

Bits

0ae5fc8e

Nonce

9,927,735

Timestamp

6/18/2017, 3:38:59 AM

Confirmations

4,660,758

Merkle Root

f06cb15a3f63bf1405a2ebb094da534b89cad9ee4b13f71b783e54976528dc25
Transactions (2)
Coinbasea2ccb3dbc7663f…e095f83d19604a
1 in β†’ 1 out8.4200 XPM110 B
AU7hZySZ…cS82Rf5w
12dc8103cc6662…705412dc1b2d12
1 in β†’ 2 out18.9801 XPM226 B
AHL3YjAe…mNZMCQnkATbraDFx…5zidfhST
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.

1.060 Γ— 10⁹⁴(95-digit number)
10601346320371617284…37645978401561326150
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
1.060 Γ— 10⁹⁴(95-digit number)
10601346320371617284…37645978401561326149
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.060 Γ— 10⁹⁴(95-digit number)
10601346320371617284…37645978401561326151
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
2.120 Γ— 10⁹⁴(95-digit number)
21202692640743234568…75291956803122652299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.120 Γ— 10⁹⁴(95-digit number)
21202692640743234568…75291956803122652301
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
4.240 Γ— 10⁹⁴(95-digit number)
42405385281486469137…50583913606245304599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.240 Γ— 10⁹⁴(95-digit number)
42405385281486469137…50583913606245304601
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
8.481 Γ— 10⁹⁴(95-digit number)
84810770562972938275…01167827212490609199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.481 Γ— 10⁹⁴(95-digit number)
84810770562972938275…01167827212490609201
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
1.696 Γ— 10⁹⁡(96-digit number)
16962154112594587655…02335654424981218399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.696 Γ— 10⁹⁡(96-digit number)
16962154112594587655…02335654424981218401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2165383

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 75313abbb41d19120b3a06e05da32a4c7e2ae9a16e8d6bf669d895a4b3b09285

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 #2,165,383 on Chainz β†—
Circulating Supply:57,853,254 XPMΒ·at block #6,826,140 Β· updates every 60s
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