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Block #2,661,501

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2018, 4:19:22 AM · Difficulty 11.6333 · 4,170,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ea0b2757a0a6cce7524261b5de470d3be8d0194173392bec3035c639c8e9c8d

View on Chainz ↗

Height

#2,661,501

Difficulty

11.633319

Transactions

Size

507 B

Version

Bits

0ba2212b

Nonce

847,832,110

Timestamp

5/15/2018, 4:19:22 AM

Confirmations

4,170,324

Merkle Root

0b56233101d6b4cf2920e387acddbc1121659ab8f95e7c2bfe690ddc357fba18

Transactions (2)

Coinbase1eacda56b8d278…05bcd3b3771d7f

1 in → 1 out7.3900 XPM110 B

AdfYGvMx…HsaszDC7

1aa1dbb9b0dd7e…55b779cc01e1ec

2 in → 2 out14.7000 XPM307 B

AQdvjBQJ…y6GLCs5n ATkwammm…oasHBd7n

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.

2.652 × 10⁹⁴(95-digit number)

26524737358021508056…55831144288934222080

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

2.652 × 10⁹⁴(95-digit number)

26524737358021508056…55831144288934222079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.652 × 10⁹⁴(95-digit number)

26524737358021508056…55831144288934222081

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

5.304 × 10⁹⁴(95-digit number)

53049474716043016113…11662288577868444159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.304 × 10⁹⁴(95-digit number)

53049474716043016113…11662288577868444161

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

1.060 × 10⁹⁵(96-digit number)

10609894943208603222…23324577155736888319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.060 × 10⁹⁵(96-digit number)

10609894943208603222…23324577155736888321

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

2.121 × 10⁹⁵(96-digit number)

21219789886417206445…46649154311473776639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.121 × 10⁹⁵(96-digit number)

21219789886417206445…46649154311473776641

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

4.243 × 10⁹⁵(96-digit number)

42439579772834412890…93298308622947553279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.243 × 10⁹⁵(96-digit number)

42439579772834412890…93298308622947553281

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

8.487 × 10⁹⁵(96-digit number)

84879159545668825781…86596617245895106559

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 2661501

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 3ea0b2757a0a6cce7524261b5de470d3be8d0194173392bec3035c639c8e9c8d

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 #2,661,501 on Chainz ↗

Block #2,661,501

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