Home/Chain Registry/Block #289,850

Block #289,850

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 9:53:31 AM · Difficulty 9.9888 · 6,503,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

607ec0f1935e0fccd07fc34e1fd8c0f7991686fe099c26d1ea6a87f144aa5bc0

View on Chainz ↗

Height

#289,850

Difficulty

9.988822

Transactions

Size

560 B

Version

Bits

09fd2369

Nonce

16,855

Timestamp

12/2/2013, 9:53:31 AM

Confirmations

6,503,237

Merkle Root

b81346b196bffb6eb21536adde2fb77c8c682073fe15a256887798229a7a3a48

Transactions (2)

Coinbase1a59ac25073ea7…9a7191655ac29c

1 in → 1 out10.0100 XPM97 B

AWQBKr3Y…sUA1Ehpd

449882d5f37ace…da5743f59be665

2 in → 2 out249.9100 XPM373 B

ATP6ihBz…va7MpWW8 AYzBVmbn…X7VDHYfx

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.

1.239 × 10⁹⁵(96-digit number)

12390640468655043840…76200372486661631220

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

1.239 × 10⁹⁵(96-digit number)

12390640468655043840…76200372486661631219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.239 × 10⁹⁵(96-digit number)

12390640468655043840…76200372486661631221

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

2.478 × 10⁹⁵(96-digit number)

24781280937310087680…52400744973323262439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.478 × 10⁹⁵(96-digit number)

24781280937310087680…52400744973323262441

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

4.956 × 10⁹⁵(96-digit number)

49562561874620175361…04801489946646524879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.956 × 10⁹⁵(96-digit number)

49562561874620175361…04801489946646524881

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

9.912 × 10⁹⁵(96-digit number)

99125123749240350723…09602979893293049759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.912 × 10⁹⁵(96-digit number)

99125123749240350723…09602979893293049761

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

1.982 × 10⁹⁶(97-digit number)

19825024749848070144…19205959786586099519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 289850

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 607ec0f1935e0fccd07fc34e1fd8c0f7991686fe099c26d1ea6a87f144aa5bc0

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 #289,850 on Chainz ↗