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Block #2,727,872

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/30/2018, 8:30:27 AM · Difficulty 11.6270 · 4,105,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

201fc52a9b5c9521caaf48a35daa33fa0f6d3ce8b09b2d0f6649505d3e6a48f0

View on Chainz ↗

Height

#2,727,872

Difficulty

11.626986

Transactions

Size

1021 B

Version

Bits

0ba08224

Nonce

127,108,776

Timestamp

6/30/2018, 8:30:27 AM

Confirmations

4,105,483

Merkle Root

62bc568120e9ba309507ca03603ecb663f0565e7c28da5ff7a1bce70daa475dd

Transactions (2)

Coinbasebae5df50633ace…e7de0679d9ab99

1 in → 1 out7.3900 XPM110 B

Ad6arkvx…LkNwQfkS

d07eaf1d2d4ac4…da797999c53573

5 in → 2 out164.0099 XPM820 B

AQmjqzoU…5U6sbve9 ANAPNfwp…XYxKXRWL

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.

4.917 × 10⁹⁶(97-digit number)

49173414414215845768…85702759290463768320

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

4.917 × 10⁹⁶(97-digit number)

49173414414215845768…85702759290463768319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.917 × 10⁹⁶(97-digit number)

49173414414215845768…85702759290463768321

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

9.834 × 10⁹⁶(97-digit number)

98346828828431691536…71405518580927536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.834 × 10⁹⁶(97-digit number)

98346828828431691536…71405518580927536641

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

1.966 × 10⁹⁷(98-digit number)

19669365765686338307…42811037161855073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.966 × 10⁹⁷(98-digit number)

19669365765686338307…42811037161855073281

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

3.933 × 10⁹⁷(98-digit number)

39338731531372676614…85622074323710146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.933 × 10⁹⁷(98-digit number)

39338731531372676614…85622074323710146561

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

7.867 × 10⁹⁷(98-digit number)

78677463062745353228…71244148647420293119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.867 × 10⁹⁷(98-digit number)

78677463062745353228…71244148647420293121

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

1.573 × 10⁹⁸(99-digit number)

15735492612549070645…42488297294840586239

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 2727872

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 201fc52a9b5c9521caaf48a35daa33fa0f6d3ce8b09b2d0f6649505d3e6a48f0

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 #2,727,872 on Chainz ↗

Block #2,727,872

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