Home/Chain Registry/Block #1,281,900

Block #1,281,900

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2015, 3:43:41 PM · Difficulty 10.8404 · 5,510,729 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b1d43867bec98c30a1620f0c26c1e976df90e3204d585788eb81808f976ca56

View on Chainz ↗

Height

#1,281,900

Difficulty

10.840395

Transactions

Size

200 B

Version

Bits

0ad7241f

Nonce

176,391,028

Timestamp

10/14/2015, 3:43:41 PM

Confirmations

5,510,729

Merkle Root

bd43b36e20d5b52c0e6196fb3f5d48bdfd68f68f78abed92924e4bda88604cc5

Transactions (1)

Coinbasebd43b36e20d5b5…4e4bda88604cc5

1 in → 1 out8.5000 XPM109 B

AK8UW42P…1RZvisiZ

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.

1.569 × 10⁹⁶(97-digit number)

15698852024950719905…64567599058134466560

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

1.569 × 10⁹⁶(97-digit number)

15698852024950719905…64567599058134466559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.569 × 10⁹⁶(97-digit number)

15698852024950719905…64567599058134466561

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

3.139 × 10⁹⁶(97-digit number)

31397704049901439810…29135198116268933119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.139 × 10⁹⁶(97-digit number)

31397704049901439810…29135198116268933121

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

6.279 × 10⁹⁶(97-digit number)

62795408099802879620…58270396232537866239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.279 × 10⁹⁶(97-digit number)

62795408099802879620…58270396232537866241

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

1.255 × 10⁹⁷(98-digit number)

12559081619960575924…16540792465075732479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.255 × 10⁹⁷(98-digit number)

12559081619960575924…16540792465075732481

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

2.511 × 10⁹⁷(98-digit number)

25118163239921151848…33081584930151464959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.511 × 10⁹⁷(98-digit number)

25118163239921151848…33081584930151464961

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 1281900

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 4b1d43867bec98c30a1620f0c26c1e976df90e3204d585788eb81808f976ca56

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 #1,281,900 on Chainz ↗