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Block #3,335,199

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/31/2019, 5:26:24 PM · Difficulty 11.0025 · 3,507,024 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7878295dd493accab0b3f5d96a0baed46860ff9ed91c0b98d85898316960e460

View on Chainz ↗

Height

#3,335,199

Difficulty

11.002461

Transactions

Size

722 B

Version

Bits

0b00a150

Nonce

945,779,555

Timestamp

8/31/2019, 5:26:24 PM

Confirmations

3,507,024

Merkle Root

ede5130c1f4ec75180e81c8723ad78598788124ffd54535aeb79a29227bb6242

Transactions (2)

Coinbased00a92e9ced8e4…beb02e679718b6

1 in → 1 out8.2600 XPM110 B

ASiq2qtK…VMhmk7yL

d9fe65bafe5853…b864d877445767

3 in → 2 out66.7296 XPM521 B

ANkkLLes…CEJqMsJZ ALZUnU38…zpTdfjSV

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.563 × 10⁹⁶(97-digit number)

35635475555478660271…98142388470350479360

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.563 × 10⁹⁶(97-digit number)

35635475555478660271…98142388470350479359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.563 × 10⁹⁶(97-digit number)

35635475555478660271…98142388470350479361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.127 × 10⁹⁶(97-digit number)

71270951110957320542…96284776940700958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.127 × 10⁹⁶(97-digit number)

71270951110957320542…96284776940700958721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.425 × 10⁹⁷(98-digit number)

14254190222191464108…92569553881401917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.425 × 10⁹⁷(98-digit number)

14254190222191464108…92569553881401917441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.850 × 10⁹⁷(98-digit number)

28508380444382928217…85139107762803834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.850 × 10⁹⁷(98-digit number)

28508380444382928217…85139107762803834881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.701 × 10⁹⁷(98-digit number)

57016760888765856434…70278215525607669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.701 × 10⁹⁷(98-digit number)

57016760888765856434…70278215525607669761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.140 × 10⁹⁸(99-digit number)

11403352177753171286…40556431051215339519

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 3335199

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 7878295dd493accab0b3f5d96a0baed46860ff9ed91c0b98d85898316960e460

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 → Debug Window → 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 #3,335,199 on Chainz ↗

Block #3,335,199

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