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Block #92,138

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 11:59:54 AM · Difficulty 9.2040 · 6,704,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc65638dacd6c5317bdccecb2614584c3d11f9ea618db8cc185ee2f6dc7ceb5b

View on Chainz ↗

Height

#92,138

Difficulty

9.204009

Transactions

Size

207 B

Version

Bits

093439ed

Nonce

178,083

Timestamp

8/1/2013, 11:59:54 AM

Confirmations

6,704,455

Merkle Root

7b780a068ced0839b20cd764b6f58cef230e454b285f6ff64354269c0debfe75

Transactions (1)

Coinbase7b780a068ced08…54269c0debfe75

1 in → 1 out11.7900 XPM109 B

AFtDEaQs…JhFmVUFn

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.

1.602 × 10¹¹³(114-digit number)

16027187521179487424…82244844287070422740

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

1.602 × 10¹¹³(114-digit number)

16027187521179487424…82244844287070422739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.602 × 10¹¹³(114-digit number)

16027187521179487424…82244844287070422741

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

3.205 × 10¹¹³(114-digit number)

32054375042358974849…64489688574140845479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.205 × 10¹¹³(114-digit number)

32054375042358974849…64489688574140845481

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

6.410 × 10¹¹³(114-digit number)

64108750084717949699…28979377148281690959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.410 × 10¹¹³(114-digit number)

64108750084717949699…28979377148281690961

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

1.282 × 10¹¹⁴(115-digit number)

12821750016943589939…57958754296563381919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.282 × 10¹¹⁴(115-digit number)

12821750016943589939…57958754296563381921

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

2.564 × 10¹¹⁴(115-digit number)

25643500033887179879…15917508593126763839

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 92138

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 bc65638dacd6c5317bdccecb2614584c3d11f9ea618db8cc185ee2f6dc7ceb5b

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 #92,138 on Chainz ↗