Block #2,876,892

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/11/2018, 3:58:44 PM · Difficulty 11.6508 · 3,966,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35a7ec321fa4f7db96efb2d927f5ce666b3a76761c8db4226cd8f82f0ce7721d

View on Chainz ↗

Height

#2,876,892

Difficulty

11.650754

Transactions

Size

1.37 KB

Version

Bits

0ba697d2

Nonce

567,542,801

Timestamp

10/11/2018, 3:58:44 PM

Confirmations

3,966,584

Mined by

⛏️ P2SHAdTbnRxdHhFWBgNMbjEwTNMsRkcZfPPG2w

Merkle Root

f4e8d839f0d25d60d005c4cc009187da3c87ec7ddd7850c7f4c6d284a3ee348a

Transactions (4)

Coinbaseb5fe4433eae909…57aba1bc78e67b

1 in → 1 out7.3800 XPM110 B

AdTbnRxd…cZfPPG2w

cbac40d8cfd0dc…0271cd452dd3de

3 in → 2 out15.0560 XPM456 B

AbNUu9xr…SFUXCj5W AedrM6jU…GYYDE6Cn

d9a24830011b08…9a1eac957824c6

1 in → 2 out4.1016 XPM226 B

Aa7Bapc9…ALDTZFjK ANFVagNM…R3Y7YPvk

085ef406931699…5e355ef9333a28

3 in → 2 out7.0819 XPM523 B

AMQEape4…7YJtWhvj AKkA4NAB…Qrms46Am

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.

4.370 × 10⁹⁷(98-digit number)

43708952805014329663…46297251902787092479

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

4.370 × 10⁹⁷(98-digit number)

43708952805014329663…46297251902787092479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.370 × 10⁹⁷(98-digit number)

43708952805014329663…46297251902787092481

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

8.741 × 10⁹⁷(98-digit number)

87417905610028659326…92594503805574184959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.741 × 10⁹⁷(98-digit number)

87417905610028659326…92594503805574184961

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

1.748 × 10⁹⁸(99-digit number)

17483581122005731865…85189007611148369919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.748 × 10⁹⁸(99-digit number)

17483581122005731865…85189007611148369921

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

3.496 × 10⁹⁸(99-digit number)

34967162244011463730…70378015222296739839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.496 × 10⁹⁸(99-digit number)

34967162244011463730…70378015222296739841

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

6.993 × 10⁹⁸(99-digit number)

69934324488022927461…40756030444593479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.993 × 10⁹⁸(99-digit number)

69934324488022927461…40756030444593479681

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

1.398 × 10⁹⁹(100-digit number)

13986864897604585492…81512060889186959359

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.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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

Cross-reference on Chainz Explorer

Block #2,876,892

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