Home/Chain Registry/Block #271,483

Block #271,483

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 4:06:12 PM · Difficulty 9.9519 · 6,528,670 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2baa5986ec6aafb22ea501b2eb31a824fad95cc70af51e00f48d1597a68cae88

View on Chainz ↗

Height

#271,483

Difficulty

9.951889

Transactions

Size

235 B

Version

Bits

09f3af00

Nonce

13,499

Timestamp

11/24/2013, 4:06:12 PM

Confirmations

6,528,670

Merkle Root

18a33c79264c4f68be7b740cdea5e20f99f8e11f724037b8d9505e2475fa0f8c

Transactions (1)

Coinbase18a33c79264c4f…505e2475fa0f8c

1 in → 2 out10.0800 XPM142 B

AdGRRh1e…QmctLb24 AU6kq4CL…dQBLvxLp

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.

1.668 × 10¹⁰¹(102-digit number)

16681704318124119206…50897372510925501890

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

1.668 × 10¹⁰¹(102-digit number)

16681704318124119206…50897372510925501889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.668 × 10¹⁰¹(102-digit number)

16681704318124119206…50897372510925501891

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

3.336 × 10¹⁰¹(102-digit number)

33363408636248238412…01794745021851003779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.336 × 10¹⁰¹(102-digit number)

33363408636248238412…01794745021851003781

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

6.672 × 10¹⁰¹(102-digit number)

66726817272496476825…03589490043702007559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.672 × 10¹⁰¹(102-digit number)

66726817272496476825…03589490043702007561

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

1.334 × 10¹⁰²(103-digit number)

13345363454499295365…07178980087404015119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.334 × 10¹⁰²(103-digit number)

13345363454499295365…07178980087404015121

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

2.669 × 10¹⁰²(103-digit number)

26690726908998590730…14357960174808030239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.669 × 10¹⁰²(103-digit number)

26690726908998590730…14357960174808030241

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 271483

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 2baa5986ec6aafb22ea501b2eb31a824fad95cc70af51e00f48d1597a68cae88

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 #271,483 on Chainz ↗