Home/Chain Registry/Block #96,571

Block #96,571

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 6:39:35 AM · Difficulty 9.2735 · 6,728,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce5c938e576f2b0fa79e194237ffa7ef0c38b4701c82871e656028ede5242676

View on Chainz ↗

Height

#96,571

Difficulty

9.273512

Transactions

Size

205 B

Version

Bits

094604de

Nonce

47,555

Timestamp

8/4/2013, 6:39:35 AM

Confirmations

6,728,527

Merkle Root

1382e6e5b3429aa75c44b8d5e68200467c16a9ac560ca4a7a3d986e7f18b92fd

Transactions (1)

Coinbase1382e6e5b3429a…d986e7f18b92fd

1 in → 1 out11.6100 XPM109 B

AdqhSCkq…FJ93rsXN

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.

1.293 × 10¹⁰⁹(110-digit number)

12936418033272770832…34145482470821181950

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

1.293 × 10¹⁰⁹(110-digit number)

12936418033272770832…34145482470821181949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.293 × 10¹⁰⁹(110-digit number)

12936418033272770832…34145482470821181951

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

2.587 × 10¹⁰⁹(110-digit number)

25872836066545541665…68290964941642363899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.587 × 10¹⁰⁹(110-digit number)

25872836066545541665…68290964941642363901

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

5.174 × 10¹⁰⁹(110-digit number)

51745672133091083330…36581929883284727799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.174 × 10¹⁰⁹(110-digit number)

51745672133091083330…36581929883284727801

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

1.034 × 10¹¹⁰(111-digit number)

10349134426618216666…73163859766569455599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.034 × 10¹¹⁰(111-digit number)

10349134426618216666…73163859766569455601

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

2.069 × 10¹¹⁰(111-digit number)

20698268853236433332…46327719533138911199

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 96571

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 ce5c938e576f2b0fa79e194237ffa7ef0c38b4701c82871e656028ede5242676

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 #96,571 on Chainz ↗

Block #96,571

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