Home/Chain Registry/Block #682,752

Block #682,752

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/18/2014, 12:48:15 PM · Difficulty 10.9604 · 6,113,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a808d84f842d34f4a85598c53a57d91bd9d51d2a73d33435e6281838ab50676

View on Chainz ↗

Height

#682,752

Difficulty

10.960424

Transactions

Size

807 B

Version

Bits

0af5de55

Nonce

3,141,358,170

Timestamp

8/18/2014, 12:48:15 PM

Confirmations

6,113,607

Merkle Root

919ac1dd871dbee504a78ac2ff9a2a1b7a7882fb014913982fff375fab9d84ad

Transactions (3)

Coinbase0b4e78ce5c8088…5e9f526fde0c27

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

7aca4d4a4d4b3d…6ecf8f7916e0da

2 in → 2 out14.5030 XPM374 B

APEp3NDq…kXkRBmWA APWbcmC1…frWY7rvy

2a11f7f945391f…2695b63e88b880

1 in → 2 out6.7548 XPM226 B

AchEXebr…mPa5Rnkp AYTox83u…uVAAM6XZ

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.

1.364 × 10⁹⁸(99-digit number)

13643940481633705293…14948422607935047680

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

1.364 × 10⁹⁸(99-digit number)

13643940481633705293…14948422607935047679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.364 × 10⁹⁸(99-digit number)

13643940481633705293…14948422607935047681

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

2.728 × 10⁹⁸(99-digit number)

27287880963267410587…29896845215870095359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.728 × 10⁹⁸(99-digit number)

27287880963267410587…29896845215870095361

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

5.457 × 10⁹⁸(99-digit number)

54575761926534821175…59793690431740190719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.457 × 10⁹⁸(99-digit number)

54575761926534821175…59793690431740190721

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

1.091 × 10⁹⁹(100-digit number)

10915152385306964235…19587380863480381439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.091 × 10⁹⁹(100-digit number)

10915152385306964235…19587380863480381441

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

2.183 × 10⁹⁹(100-digit number)

21830304770613928470…39174761726960762879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.183 × 10⁹⁹(100-digit number)

21830304770613928470…39174761726960762881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.366 × 10⁹⁹(100-digit number)

43660609541227856940…78349523453921525759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 682752

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 3a808d84f842d34f4a85598c53a57d91bd9d51d2a73d33435e6281838ab50676

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 #682,752 on Chainz ↗