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Home/Chain Registry/Block #2,730,984

Block #2,730,984

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/2/2018, 11:23:40 AM Β· Difficulty 11.6314 Β· 4,107,728 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
918286172440b150adeb1488b92a3c1d979e1cef74da24a967896dabd26773e5
View on Chainz β†—

Difficulty

11.631440

Transactions

1

Size

200 B

Version

2

Bits

0ba1a613

Nonce

495,099,001

Timestamp

7/2/2018, 11:23:40 AM

Confirmations

4,107,728

Merkle Root

91b4a83d9c03023f1a97ecf458c82127dd8dc49661196da04d272052273d8c4d
Transactions (1)
Coinbase91b4a83d9c0302…272052273d8c4d
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171200
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
2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171201
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
5.684 Γ— 10⁹⁴(95-digit number)
56844596078217810629…56820940438042342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.684 Γ— 10⁹⁴(95-digit number)
56844596078217810629…56820940438042342401
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
1.136 Γ— 10⁹⁡(96-digit number)
11368919215643562125…13641880876084684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.136 Γ— 10⁹⁡(96-digit number)
11368919215643562125…13641880876084684801
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
2.273 Γ— 10⁹⁡(96-digit number)
22737838431287124251…27283761752169369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.273 Γ— 10⁹⁡(96-digit number)
22737838431287124251…27283761752169369601
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
4.547 Γ— 10⁹⁡(96-digit number)
45475676862574248503…54567523504338739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.547 Γ— 10⁹⁡(96-digit number)
45475676862574248503…54567523504338739201
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
9.095 Γ— 10⁹⁡(96-digit number)
90951353725148497007…09135047008677478399
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 2730984

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 918286172440b150adeb1488b92a3c1d979e1cef74da24a967896dabd26773e5

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 #2,730,984 on Chainz β†—
Circulating Supply:57,953,963 XPMΒ·at block #6,838,711 Β· updates every 60s
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