Block #1,340,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2015, 10:04:20 PM · Difficulty 10.7997 · 5,468,069 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db8464231c40366dde8a8d9589b7d60c635fc657142f66617ad90997b09b955d

View on Chainz ↗

Height

#1,340,112

Difficulty

10.799735

Transactions

Size

1.45 KB

Version

Bits

0accbb76

Nonce

574,978,462

Timestamp

11/24/2015, 10:04:20 PM

Confirmations

5,468,069

Mined by

⛏️ P2SHAXjKmSXXwP1Ysw582Sws6BW99Uhv4SJfSr

Merkle Root

f549941546b8e8b4d2920eda9ce9fcd64356a826f5d8474a2d5ef278372c9aa6

Transactions (2)

Coinbase4d73db56986c39…8990260cd000f0

1 in → 1 out8.5800 XPM110 B

AXjKmSXX…hv4SJfSr

b9488241bc9331…32188736a74dc2

1 in → 33 out14.3039 XPM1.25 KB

AX4UAthk…SJTV3sAG AcyWLcPW…MBkw4RHa AU1DVCYZ…Cr53tDSS AZcvXaEC…gstDfNmL AMfPEFty…MoiGTaKf

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.

5.104 × 10⁹⁵(96-digit number)

51046418315538642598…90528228250371358719

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

5.104 × 10⁹⁵(96-digit number)

51046418315538642598…90528228250371358719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.104 × 10⁹⁵(96-digit number)

51046418315538642598…90528228250371358721

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

1.020 × 10⁹⁶(97-digit number)

10209283663107728519…81056456500742717439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.020 × 10⁹⁶(97-digit number)

10209283663107728519…81056456500742717441

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

2.041 × 10⁹⁶(97-digit number)

20418567326215457039…62112913001485434879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.041 × 10⁹⁶(97-digit number)

20418567326215457039…62112913001485434881

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

4.083 × 10⁹⁶(97-digit number)

40837134652430914078…24225826002970869759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.083 × 10⁹⁶(97-digit number)

40837134652430914078…24225826002970869761

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

8.167 × 10⁹⁶(97-digit number)

81674269304861828157…48451652005941739519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.167 × 10⁹⁶(97-digit number)

81674269304861828157…48451652005941739521

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 #1,340,112

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