Block #1,694,534

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/29/2016, 8:54:18 PM · Difficulty 10.6800 · 5,120,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0554289b7876c781f8a841cbb4f1d3e64b4f6ef7c0edd8d9d87a89f9dd75da7

View on Chainz ↗

Height

#1,694,534

Difficulty

10.680025

Transactions

Size

3.67 KB

Version

Bits

0aae161e

Nonce

253,064,051

Timestamp

7/29/2016, 8:54:18 PM

Confirmations

5,120,606

Mined by

⛏️ P2SHAY8Xva2tkrMxJ8TYSf7LyNtyUJiU8PqjFw

Merkle Root

7ce0020b73c9f39e60740b415cd142d70b2e89f87e1bc37137de50f99161a421

Transactions (3)

Coinbase574dae5ba307d9…82f9405e891610

1 in → 1 out8.8000 XPM109 B

AY8Xva2t…iU8PqjFw

5ae45713fceb69…abd71319d95876

1 in → 40 out70.4747 XPM1.48 KB

AVREYKHU…JZxbKnN9 AVrgYA3s…tnVYvavw AdHGoCme…rZ4SeUXP AeyJqMQq…eh5iKkdh AWyxhEMs…6zgbhMhR

43e838c1fc4d1c…7fb56adf44e8bc

2 in → 51 out1.9312 XPM1.99 KB

AbqwBWfR…gcNMU5RN ARb2Whmi…3eQaSMW4 AYnEx4MZ…D6LtC628 AQVxtL9k…KzYw3SKu AcYe7uoE…vRsnGDKZ

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.

8.306 × 10⁹⁵(96-digit number)

83060603891126063437…02753031107149552639

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

8.306 × 10⁹⁵(96-digit number)

83060603891126063437…02753031107149552639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.306 × 10⁹⁵(96-digit number)

83060603891126063437…02753031107149552641

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

1.661 × 10⁹⁶(97-digit number)

16612120778225212687…05506062214299105279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.661 × 10⁹⁶(97-digit number)

16612120778225212687…05506062214299105281

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

3.322 × 10⁹⁶(97-digit number)

33224241556450425375…11012124428598210559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.322 × 10⁹⁶(97-digit number)

33224241556450425375…11012124428598210561

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

6.644 × 10⁹⁶(97-digit number)

66448483112900850750…22024248857196421119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.644 × 10⁹⁶(97-digit number)

66448483112900850750…22024248857196421121

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

1.328 × 10⁹⁷(98-digit number)

13289696622580170150…44048497714392842239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.328 × 10⁹⁷(98-digit number)

13289696622580170150…44048497714392842241

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 #1,694,534

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