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Block #2,716,658

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/22/2018, 4:30:24 PM · Difficulty 11.6135 · 4,123,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ff6238d5fca3ee10efc091a15068742789306b026104f1ead825d092387b688

View on Chainz ↗

Height

#2,716,658

Difficulty

11.613508

Transactions

Size

573 B

Version

Bits

0b9d0ede

Nonce

178,882,628

Timestamp

6/22/2018, 4:30:24 PM

Confirmations

4,123,738

Merkle Root

b6477f21f0457a1e0517b7ab5eb4834591509b129ff7265c84d7a083b51f66d0

Transactions (2)

Coinbasee4b5e7dc41c137…89a4997c0c34f5

1 in → 1 out7.4100 XPM110 B

AMzHpGFf…jTriBkJj

268012e95abd36…6bd5d786141e25

2 in → 2 out565.0061 XPM373 B

AbKFvGKV…eL3bdfEb AGJkwxn2…vMYNyZPm

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.

2.631 × 10⁹⁵(96-digit number)

26317878707236170517…05306586226560148640

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

2.631 × 10⁹⁵(96-digit number)

26317878707236170517…05306586226560148639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.631 × 10⁹⁵(96-digit number)

26317878707236170517…05306586226560148641

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

5.263 × 10⁹⁵(96-digit number)

52635757414472341035…10613172453120297279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.263 × 10⁹⁵(96-digit number)

52635757414472341035…10613172453120297281

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

1.052 × 10⁹⁶(97-digit number)

10527151482894468207…21226344906240594559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.052 × 10⁹⁶(97-digit number)

10527151482894468207…21226344906240594561

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

2.105 × 10⁹⁶(97-digit number)

21054302965788936414…42452689812481189119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.105 × 10⁹⁶(97-digit number)

21054302965788936414…42452689812481189121

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

4.210 × 10⁹⁶(97-digit number)

42108605931577872828…84905379624962378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.210 × 10⁹⁶(97-digit number)

42108605931577872828…84905379624962378241

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

8.421 × 10⁹⁶(97-digit number)

84217211863155745657…69810759249924756479

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 2716658

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 2ff6238d5fca3ee10efc091a15068742789306b026104f1ead825d092387b688

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 #2,716,658 on Chainz ↗

Block #2,716,658

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