Block #1,744,297

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/1/2016, 11:42:50 PM · Difficulty 10.7195 · 5,068,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff0ef601a44e2c9ef6da8de68d6abfa8b58a4a000eb0522a31098113cc97e281

View on Chainz ↗

Height

#1,744,297

Difficulty

10.719471

Transactions

Size

5.47 KB

Version

Bits

0ab82f40

Nonce

1,547,344,110

Timestamp

9/1/2016, 11:42:50 PM

Confirmations

5,068,750

Mined by

⛏️ P2SHAGLGHtKzhHtiW3LzB9xGydPnkbhtStNm1J

Merkle Root

1d2a5fcb38290d40abe6421def17067d1ebb810123e6a3c3c6fab5c5f1292679

Transactions (2)

Coinbase0827f4faed8fe4…2e86809bcb9485

1 in → 1 out8.7500 XPM109 B

AGLGHtKz…htStNm1J

9d56416c8c4a06…5f2e68badc63d7

36 in → 2 out289.2510 XPM5.27 KB

AN813yZG…zMYimtUr AdvLfhqF…YUuRFQZL

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.

3.537 × 10⁹⁶(97-digit number)

35375204524145963296…38509595889388789759

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

3.537 × 10⁹⁶(97-digit number)

35375204524145963296…38509595889388789759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.537 × 10⁹⁶(97-digit number)

35375204524145963296…38509595889388789761

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

7.075 × 10⁹⁶(97-digit number)

70750409048291926593…77019191778777579519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.075 × 10⁹⁶(97-digit number)

70750409048291926593…77019191778777579521

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

1.415 × 10⁹⁷(98-digit number)

14150081809658385318…54038383557555159039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.415 × 10⁹⁷(98-digit number)

14150081809658385318…54038383557555159041

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

2.830 × 10⁹⁷(98-digit number)

28300163619316770637…08076767115110318079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.830 × 10⁹⁷(98-digit number)

28300163619316770637…08076767115110318081

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

5.660 × 10⁹⁷(98-digit number)

56600327238633541274…16153534230220636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.660 × 10⁹⁷(98-digit number)

56600327238633541274…16153534230220636161

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 #1,744,297

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