Home/Chain Registry/Block #433,537

Block #433,537

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 3:49:03 PM · Difficulty 10.3451 · 6,359,458 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac159ec066be6eb695a6eba6849aff30d22af9478de33d0bd3215f0405532bc7

View on Chainz ↗

Height

#433,537

Difficulty

10.345130

Transactions

Size

187 B

Version

Bits

0a585a6f

Nonce

162,358

Timestamp

3/7/2014, 3:49:03 PM

Confirmations

6,359,458

Merkle Root

ec394e1bf8acb94bd1fa7fe58ea08dc7308ecd2e61dbed90261a5ebf0e50ef8e

Transactions (1)

Coinbaseec394e1bf8acb9…1a5ebf0e50ef8e

1 in → 1 out9.3300 XPM97 B

AYCeLhqB…eqGM6KK1

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.

3.852 × 10⁹⁵(96-digit number)

38529580299096304849…76634709513328843280

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

3.852 × 10⁹⁵(96-digit number)

38529580299096304849…76634709513328843279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.852 × 10⁹⁵(96-digit number)

38529580299096304849…76634709513328843281

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

7.705 × 10⁹⁵(96-digit number)

77059160598192609699…53269419026657686559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.705 × 10⁹⁵(96-digit number)

77059160598192609699…53269419026657686561

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

1.541 × 10⁹⁶(97-digit number)

15411832119638521939…06538838053315373119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.541 × 10⁹⁶(97-digit number)

15411832119638521939…06538838053315373121

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

3.082 × 10⁹⁶(97-digit number)

30823664239277043879…13077676106630746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.082 × 10⁹⁶(97-digit number)

30823664239277043879…13077676106630746241

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

6.164 × 10⁹⁶(97-digit number)

61647328478554087759…26155352213261492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.164 × 10⁹⁶(97-digit number)

61647328478554087759…26155352213261492481

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 433537

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 ac159ec066be6eb695a6eba6849aff30d22af9478de33d0bd3215f0405532bc7

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 #433,537 on Chainz ↗