Home/Chain Registry/Block #90,151

Block #90,151

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 9:39:15 PM · Difficulty 9.2518 · 6,699,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbd781ee92cc1141f0f28c053f7b8def54a4016f3d1c0880810dadf3d3833202

View on Chainz ↗

Height

#90,151

Difficulty

9.251760

Transactions

Size

200 B

Version

Bits

09407357

Nonce

Timestamp

7/30/2013, 9:39:15 PM

Confirmations

6,699,898

Merkle Root

cfd7781bd1d667ed67f02ccaf82063bb67170bfd568778bb30b85c84f2619741

Transactions (1)

Coinbasecfd7781bd1d667…b85c84f2619741

1 in → 1 out11.6700 XPM110 B

AZHSwYNo…p3tcGZ3E

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.

4.382 × 10⁹⁵(96-digit number)

43825453813504677423…45722637869127651660

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

4.382 × 10⁹⁵(96-digit number)

43825453813504677423…45722637869127651659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.382 × 10⁹⁵(96-digit number)

43825453813504677423…45722637869127651661

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

8.765 × 10⁹⁵(96-digit number)

87650907627009354846…91445275738255303319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.765 × 10⁹⁵(96-digit number)

87650907627009354846…91445275738255303321

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

1.753 × 10⁹⁶(97-digit number)

17530181525401870969…82890551476510606639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.753 × 10⁹⁶(97-digit number)

17530181525401870969…82890551476510606641

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

3.506 × 10⁹⁶(97-digit number)

35060363050803741938…65781102953021213279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.506 × 10⁹⁶(97-digit number)

35060363050803741938…65781102953021213281

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

7.012 × 10⁹⁶(97-digit number)

70120726101607483877…31562205906042426559

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 90151

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 bbd781ee92cc1141f0f28c053f7b8def54a4016f3d1c0880810dadf3d3833202

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 #90,151 on Chainz ↗