Block #2,088,297

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2017, 6:10:37 AM · Difficulty 10.8753 · 4,748,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3741fa208c96773e42c568af2d31fe17f2052c69bb429fa3ebd2aabc45e2b52c

View on Chainz ↗

Height

#2,088,297

Difficulty

10.875261

Transactions

Size

653 B

Version

Bits

0ae0111c

Nonce

1,240,584,550

Timestamp

4/26/2017, 6:10:37 AM

Confirmations

4,748,847

Mined by

⛏️ P2SHAUbGQiRwUy1MkoPPDFUy6A8Xc96jCiQQHL

Merkle Root

af82ee359fe89140d5c5b4b32b6c2c2de0599a3aecd8a9e67169e830bb0dbca9

Transactions (3)

Coinbase34c434c1eb335e…8aa3d5b411f764

1 in → 1 out8.4600 XPM110 B

AUbGQiRw…6jCiQQHL

83ef98a5674d27…309b12643b6c18

1 in → 2 out494.9900 XPM226 B

AbPivBQC…jYz9BW8g AWmF7BSi…NxGGG3Ls

b0e096960a9ab6…a8b6a04c4f75c1

1 in → 2 out2855.3385 XPM227 B

Adcymibw…WSNVjt24 AaLEkvYG…cxMw1E1A

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.

1.119 × 10⁹⁵(96-digit number)

11197372425308721303…12983353926659713599

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

1.119 × 10⁹⁵(96-digit number)

11197372425308721303…12983353926659713599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.119 × 10⁹⁵(96-digit number)

11197372425308721303…12983353926659713601

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

2.239 × 10⁹⁵(96-digit number)

22394744850617442606…25966707853319427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.239 × 10⁹⁵(96-digit number)

22394744850617442606…25966707853319427201

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

4.478 × 10⁹⁵(96-digit number)

44789489701234885212…51933415706638854399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.478 × 10⁹⁵(96-digit number)

44789489701234885212…51933415706638854401

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

8.957 × 10⁹⁵(96-digit number)

89578979402469770424…03866831413277708799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.957 × 10⁹⁵(96-digit number)

89578979402469770424…03866831413277708801

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

1.791 × 10⁹⁶(97-digit number)

17915795880493954084…07733662826555417599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.791 × 10⁹⁶(97-digit number)

17915795880493954084…07733662826555417601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,088,297

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