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Home/Chain Registry/Block #3,364,737

Block #3,364,737

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2019, 7:56:54 AM Β· Difficulty 10.9954 Β· 3,462,396 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
894024d1426992df3d7892bd37a3f5cb4c80d0b3925fdb1619696de7d3a1a4f4
View on Chainz β†—

Difficulty

10.995448

Transactions

1

Size

201 B

Version

2

Bits

0afed5a9

Nonce

231,797,589

Timestamp

9/22/2019, 7:56:54 AM

Confirmations

3,462,396

Merkle Root

987b5ec0f9678201f9b1934cfa583e246e47053896732a6379235e619bb5d6b5
Transactions (1)
Coinbase987b5ec0f96782…235e619bb5d6b5
1 in β†’ 1 out8.2600 XPM110 B
AXfJqzUb…HXeXmjMz
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.

5.887 Γ— 10⁹⁷(98-digit number)
58878111888287953416…00295672095743590400
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
5.887 Γ— 10⁹⁷(98-digit number)
58878111888287953416…00295672095743590399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.887 Γ— 10⁹⁷(98-digit number)
58878111888287953416…00295672095743590401
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
1.177 Γ— 10⁹⁸(99-digit number)
11775622377657590683…00591344191487180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.177 Γ— 10⁹⁸(99-digit number)
11775622377657590683…00591344191487180801
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
2.355 Γ— 10⁹⁸(99-digit number)
23551244755315181366…01182688382974361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.355 Γ— 10⁹⁸(99-digit number)
23551244755315181366…01182688382974361601
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
4.710 Γ— 10⁹⁸(99-digit number)
47102489510630362732…02365376765948723199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.710 Γ— 10⁹⁸(99-digit number)
47102489510630362732…02365376765948723201
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
9.420 Γ— 10⁹⁸(99-digit number)
94204979021260725465…04730753531897446399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.420 Γ— 10⁹⁸(99-digit number)
94204979021260725465…04730753531897446401
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
1.884 Γ— 10⁹⁹(100-digit number)
18840995804252145093…09461507063794892799
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 3364737

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 894024d1426992df3d7892bd37a3f5cb4c80d0b3925fdb1619696de7d3a1a4f4

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 #3,364,737 on Chainz β†—
Circulating Supply:57,861,244 XPMΒ·at block #6,827,132 Β· updates every 60s
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