Home/Chain Registry/Block #85,645

Block #85,645

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 1:59:53 PM · Difficulty 9.2911 · 6,704,028 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df0f99fc0f634d974d09f3252cd2021ece12e71c3e659408b27feb375cb63d7e

View on Chainz ↗

Height

#85,645

Difficulty

9.291051

Transactions

Size

1.29 KB

Version

Bits

094a824d

Nonce

39,376

Timestamp

7/27/2013, 1:59:53 PM

Confirmations

6,704,028

Merkle Root

feec14723b1136744128fe867748cea82c79a5618205f47dc698073a108b48c9

Transactions (3)

Coinbased4216b7cf6064d…f589efdcc2ffff

1 in → 1 out11.5900 XPM109 B

AZJK9yNS…5mBQm6oL

ba2c37ea6c69a9…93a08ea5ee8f5d

1 in → 1 out11.6100 XPM158 B

AH9D5N1B…4NXoLsWQ

7b98e9df73ea70…e7e95bbbb69777

6 in → 2 out2.3034 XPM965 B

AaCZiFay…6oNYPY5h AG2dvTg9…xrF4dkzJ

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.

2.318 × 10⁹⁷(98-digit number)

23187801638153953277…81153863879550046800

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

2.318 × 10⁹⁷(98-digit number)

23187801638153953277…81153863879550046799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.318 × 10⁹⁷(98-digit number)

23187801638153953277…81153863879550046801

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

4.637 × 10⁹⁷(98-digit number)

46375603276307906554…62307727759100093599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.637 × 10⁹⁷(98-digit number)

46375603276307906554…62307727759100093601

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

9.275 × 10⁹⁷(98-digit number)

92751206552615813108…24615455518200187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.275 × 10⁹⁷(98-digit number)

92751206552615813108…24615455518200187201

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

1.855 × 10⁹⁸(99-digit number)

18550241310523162621…49230911036400374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.855 × 10⁹⁸(99-digit number)

18550241310523162621…49230911036400374401

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

3.710 × 10⁹⁸(99-digit number)

37100482621046325243…98461822072800748799

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 85645

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 df0f99fc0f634d974d09f3252cd2021ece12e71c3e659408b27feb375cb63d7e

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 #85,645 on Chainz ↗