Block #1,340,771

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2015, 8:08:58 AM · Difficulty 10.8020 · 5,471,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b259bbc4c16305cce0f581fe82705e2b767aded82bbc8f057a3a1dcea99708a1

View on Chainz ↗

Height

#1,340,771

Difficulty

10.802026

Transactions

Size

5.68 KB

Version

Bits

0acd5199

Nonce

1,311,283,902

Timestamp

11/25/2015, 8:08:58 AM

Confirmations

5,471,838

Mined by

⛏️ P2SHAK6Fhb5D7fbajS5to8oibuYX4HmCaJBwSx

Merkle Root

71881a9844a60732fe307ad41cf4926070a44032d605205fe392f475c8862cc8

Transactions (3)

Coinbase304bad90ec2160…d381bf2078c283

1 in → 1 out8.6200 XPM109 B

AK6Fhb5D…mCaJBwSx

a9bd174e97d35d…04b36b52780a2a

1 in → 44 out39.8994 XPM1.61 KB

Acrguupx…ojdA3kXt AWJs3qth…wZrJpDUx ALjtDzbN…72u9Uf6h ASmGtW9o…CLgBvz51 AcyWLcPW…MBkw4RHa

1b0a257e16fef5…51baf8606e017d

15 in → 51 out3.0373 XPM3.87 KB

ActV8G5m…tj5GUMNj AGNi1BJk…5rveYCrj AURoW9Yc…sDmzUwuj AWzVmL1L…gGq1farc AbdJT9zW…SXepdTCC

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.

1.752 × 10⁹⁵(96-digit number)

17523321927164050670…90955492475581713439

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

1.752 × 10⁹⁵(96-digit number)

17523321927164050670…90955492475581713439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.752 × 10⁹⁵(96-digit number)

17523321927164050670…90955492475581713441

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

3.504 × 10⁹⁵(96-digit number)

35046643854328101340…81910984951163426879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.504 × 10⁹⁵(96-digit number)

35046643854328101340…81910984951163426881

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

7.009 × 10⁹⁵(96-digit number)

70093287708656202681…63821969902326853759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.009 × 10⁹⁵(96-digit number)

70093287708656202681…63821969902326853761

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

1.401 × 10⁹⁶(97-digit number)

14018657541731240536…27643939804653707519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.401 × 10⁹⁶(97-digit number)

14018657541731240536…27643939804653707521

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

2.803 × 10⁹⁶(97-digit number)

28037315083462481072…55287879609307415039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.803 × 10⁹⁶(97-digit number)

28037315083462481072…55287879609307415041

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 #1,340,771

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