Block #364,006

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 6:55:56 PM · Difficulty 10.4196 · 6,434,809 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88c160bb5b17b06abcbf26d9d43e3180804caf7bdca68a7e9d655450c5415b6a

View on Chainz ↗

Height

#364,006

Difficulty

10.419602

Transactions

Size

867 B

Version

Bits

0a6b6b0b

Nonce

325,921

Timestamp

1/17/2014, 6:55:56 PM

Confirmations

6,434,809

Mined by

AM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

6f570b320231b208ba062c1b495594b67610fabedfd446af0486d2e07ec09a67

Transactions (1)

Coinbase6f570b320231b2…86d2e07ec09a67

1 in → 21 out9.2000 XPM777 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF APFsQ3Fo…xoFKrF12 ANVG1nLa…Mo7dugCD AL2a2TYD…f9sjcukW

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.

8.409 × 10⁹⁴(95-digit number)

84090385937623514988…97184415499122832259

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

8.409 × 10⁹⁴(95-digit number)

84090385937623514988…97184415499122832259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.409 × 10⁹⁴(95-digit number)

84090385937623514988…97184415499122832261

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

1.681 × 10⁹⁵(96-digit number)

16818077187524702997…94368830998245664519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.681 × 10⁹⁵(96-digit number)

16818077187524702997…94368830998245664521

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

3.363 × 10⁹⁵(96-digit number)

33636154375049405995…88737661996491329039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.363 × 10⁹⁵(96-digit number)

33636154375049405995…88737661996491329041

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

6.727 × 10⁹⁵(96-digit number)

67272308750098811990…77475323992982658079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.727 × 10⁹⁵(96-digit number)

67272308750098811990…77475323992982658081

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

1.345 × 10⁹⁶(97-digit number)

13454461750019762398…54950647985965316159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.345 × 10⁹⁶(97-digit number)

13454461750019762398…54950647985965316161

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