Block #1,796,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2016, 6:14:03 PM · Difficulty 10.7760 · 5,020,281 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a571232865659bdd2fad58ded66c5278ccc5d40f17076d2558a0d00df6f3ec43

View on Chainz ↗

Height

#1,796,909

Difficulty

10.776024

Transactions

Size

3.89 KB

Version

Bits

0ac6a97e

Nonce

879,250,541

Timestamp

10/7/2016, 6:14:03 PM

Confirmations

5,020,281

Mined by

⛏️ P2SHANHqfnhqNZqyhZL7ncn1JqF53C9vEeVaef

Merkle Root

49b99993d53976694bf3296ff12820fd657c44bc56a11735dd363c101764c4a0

Transactions (3)

Coinbase1ade3874ae4592…f842fe1f5861d6

1 in → 1 out8.6400 XPM110 B

ANHqfnhq…9vEeVaef

2dc01b3cda0b09…e68045536b81ce

1 in → 51 out47.1300 XPM1.85 KB

AS1jttz1…JfswEXes ALZFCPc7…8m3ZmPFe AbNuqa5C…Fn7gDdDx ASK96rTz…VHUWZ2Tj AJFvmRUX…MFSm3Czo

88618ca0aa17a9…fdef9a2217aa2a

1 in → 51 out34.8553 XPM1.85 KB

ASPxuxyy…f1CNegsf ARhjHwur…ZN6FkD1m ATtYYXgt…UZV5hD19 AR3WdZjd…NY2wnTQG APde3AAJ…wAC8gqU9

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.

3.409 × 10⁹⁷(98-digit number)

34094834984301603642…89008010341129379839

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

3.409 × 10⁹⁷(98-digit number)

34094834984301603642…89008010341129379839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.409 × 10⁹⁷(98-digit number)

34094834984301603642…89008010341129379841

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

6.818 × 10⁹⁷(98-digit number)

68189669968603207285…78016020682258759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.818 × 10⁹⁷(98-digit number)

68189669968603207285…78016020682258759681

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

1.363 × 10⁹⁸(99-digit number)

13637933993720641457…56032041364517519359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.363 × 10⁹⁸(99-digit number)

13637933993720641457…56032041364517519361

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

2.727 × 10⁹⁸(99-digit number)

27275867987441282914…12064082729035038719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.727 × 10⁹⁸(99-digit number)

27275867987441282914…12064082729035038721

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

5.455 × 10⁹⁸(99-digit number)

54551735974882565828…24128165458070077439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.455 × 10⁹⁸(99-digit number)

54551735974882565828…24128165458070077441

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 #1,796,909

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