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Block #6,784,923

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2026, 10:45:07 PM · Difficulty 10.9809 · 7,420 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df560604e2bfe9a11aa7081b7ed0007ddf539a6e20d82a35f08aa4967c97a69c

View on Chainz ↗

Height

#6,784,923

Difficulty

10.980868

Transactions

Size

191 B

Version

536870912

Bits

0afb1a22

Nonce

822,045,712

Timestamp

4/5/2026, 10:45:07 PM

Confirmations

7,420

Merkle Root

59ee67b52d9f22238d3482ea2463d36d3d4cc43bad6769f9881abe5a0aa26ee9

Transactions (1)

Coinbase59ee67b52d9f22…1abe5a0aa26ee9

1 in → 1 out8.1790 XPM101 B

AMrLYUQN…jwjifxiz

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.

3.840 × 10⁹⁵(96-digit number)

38405104582866981163…50057117142455040000

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

3.840 × 10⁹⁵(96-digit number)

38405104582866981163…50057117142455039999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.840 × 10⁹⁵(96-digit number)

38405104582866981163…50057117142455040001

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

7.681 × 10⁹⁵(96-digit number)

76810209165733962327…00114234284910079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.681 × 10⁹⁵(96-digit number)

76810209165733962327…00114234284910080001

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

1.536 × 10⁹⁶(97-digit number)

15362041833146792465…00228468569820159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.536 × 10⁹⁶(97-digit number)

15362041833146792465…00228468569820160001

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

3.072 × 10⁹⁶(97-digit number)

30724083666293584930…00456937139640319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.072 × 10⁹⁶(97-digit number)

30724083666293584930…00456937139640320001

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

6.144 × 10⁹⁶(97-digit number)

61448167332587169861…00913874279280639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.144 × 10⁹⁶(97-digit number)

61448167332587169861…00913874279280640001

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

1.228 × 10⁹⁷(98-digit number)

12289633466517433972…01827748558561279999

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 6784923

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 df560604e2bfe9a11aa7081b7ed0007ddf539a6e20d82a35f08aa4967c97a69c

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 #6,784,923 on Chainz ↗