Home/Chain Registry/Block #91,986

Block #91,986

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 8:57:16 AM · Difficulty 9.2090 · 6,721,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0a68225761bbc8102d9e53320f8d3dbf0aac5c23b7c6e570a4bcc3b6e2a4a1c

View on Chainz ↗

Height

#91,986

Difficulty

9.208968

Transactions

Size

429 B

Version

Bits

09357eee

Nonce

28,473

Timestamp

8/1/2013, 8:57:16 AM

Confirmations

6,721,918

Merkle Root

0ea5a2b368bf8916202392554dc5100c67da7654542f8ca29e06671bf34bfcf6

Transactions (2)

Coinbase56bd41e605a642…a3d25a18717593

1 in → 1 out11.7800 XPM109 B

AV6kMea3…WSpjvkb2

cb541aeef5f24e…5a57fadd5e27f7

1 in → 2 out309.9851 XPM225 B

AQXzd9dK…23VhnKTX ANokenZx…sNgASSEm

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.

5.136 × 10¹⁰⁷(108-digit number)

51363449552480505938…35224859561720284660

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

5.136 × 10¹⁰⁷(108-digit number)

51363449552480505938…35224859561720284659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.136 × 10¹⁰⁷(108-digit number)

51363449552480505938…35224859561720284661

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

1.027 × 10¹⁰⁸(109-digit number)

10272689910496101187…70449719123440569319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.027 × 10¹⁰⁸(109-digit number)

10272689910496101187…70449719123440569321

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

2.054 × 10¹⁰⁸(109-digit number)

20545379820992202375…40899438246881138639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.054 × 10¹⁰⁸(109-digit number)

20545379820992202375…40899438246881138641

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

4.109 × 10¹⁰⁸(109-digit number)

41090759641984404751…81798876493762277279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.109 × 10¹⁰⁸(109-digit number)

41090759641984404751…81798876493762277281

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

8.218 × 10¹⁰⁸(109-digit number)

82181519283968809502…63597752987524554559

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 91986

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 a0a68225761bbc8102d9e53320f8d3dbf0aac5c23b7c6e570a4bcc3b6e2a4a1c

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 #91,986 on Chainz ↗

Block #91,986

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