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Block #83,267

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 12:50:23 AM · Difficulty 9.2697 · 6,743,249 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

352b39811a555f31ebdb77d30e168644aa95329a43a9289cbe73d362cf243418

View on Chainz ↗

Height

#83,267

Difficulty

9.269690

Transactions

Size

211 B

Version

Bits

09450a6a

Nonce

1,327

Timestamp

7/26/2013, 12:50:23 AM

Confirmations

6,743,249

Merkle Root

2248c260ff52aa0f96e2cc3fe61f49cc7377c1d8d233de9f24abc6e6d6960cf3

Transactions (1)

Coinbase2248c260ff52aa…abc6e6d6960cf3

1 in → 1 out11.6200 XPM110 B

Aec1bBfv…5BJM96CV

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.

1.978 × 10¹²²(123-digit number)

19785183081937202005…48393153627066389120

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

1.978 × 10¹²²(123-digit number)

19785183081937202005…48393153627066389119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.978 × 10¹²²(123-digit number)

19785183081937202005…48393153627066389121

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

3.957 × 10¹²²(123-digit number)

39570366163874404010…96786307254132778239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.957 × 10¹²²(123-digit number)

39570366163874404010…96786307254132778241

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

7.914 × 10¹²²(123-digit number)

79140732327748808020…93572614508265556479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.914 × 10¹²²(123-digit number)

79140732327748808020…93572614508265556481

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

1.582 × 10¹²³(124-digit number)

15828146465549761604…87145229016531112959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.582 × 10¹²³(124-digit number)

15828146465549761604…87145229016531112961

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

3.165 × 10¹²³(124-digit number)

31656292931099523208…74290458033062225919

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 83267

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 352b39811a555f31ebdb77d30e168644aa95329a43a9289cbe73d362cf243418

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 #83,267 on Chainz ↗

Block #83,267

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