Home/Chain Registry/Block #2,054,336

Block #2,054,336

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 4/4/2017, 10:36:00 AM · Difficulty 10.7915 · 4,787,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86527be5e45fc5b5dfb5b341c222b4bf3957dd5f5f28ccb0103d222c1ecb7221

View on Chainz ↗

Height

#2,054,336

Difficulty

10.791496

Transactions

Size

200 B

Version

Bits

0aca9f73

Nonce

44,621,330

Timestamp

4/4/2017, 10:36:00 AM

Confirmations

4,787,631

Merkle Root

67b8ea66337e79bfdaa6d314b3dd8562cc1e1f3a7cfa5f6e0c7aa7a02bfddc71

Transactions (1)

Coinbase67b8ea66337e79…7aa7a02bfddc71

1 in → 1 out8.5700 XPM110 B

AUTt8dEy…jgMf8tWE

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.

1.372 × 10⁹⁵(96-digit number)

13726329388636322718…57298899795124008000

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

1.372 × 10⁹⁵(96-digit number)

13726329388636322718…57298899795124007999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.372 × 10⁹⁵(96-digit number)

13726329388636322718…57298899795124008001

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

2.745 × 10⁹⁵(96-digit number)

27452658777272645436…14597799590248015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.745 × 10⁹⁵(96-digit number)

27452658777272645436…14597799590248016001

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

5.490 × 10⁹⁵(96-digit number)

54905317554545290872…29195599180496031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.490 × 10⁹⁵(96-digit number)

54905317554545290872…29195599180496032001

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

1.098 × 10⁹⁶(97-digit number)

10981063510909058174…58391198360992063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.098 × 10⁹⁶(97-digit number)

10981063510909058174…58391198360992064001

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

2.196 × 10⁹⁶(97-digit number)

21962127021818116348…16782396721984127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.196 × 10⁹⁶(97-digit number)

21962127021818116348…16782396721984128001

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

4.392 × 10⁹⁶(97-digit number)

43924254043636232697…33564793443968255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.392 × 10⁹⁶(97-digit number)

43924254043636232697…33564793443968256001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 2054336

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 86527be5e45fc5b5dfb5b341c222b4bf3957dd5f5f28ccb0103d222c1ecb7221

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 #2,054,336 on Chainz ↗

Block #2,054,336

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