Block #298,158

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 3:45:03 AM · Difficulty 9.9919 · 6,511,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60a987866c4d7bbdb567d1742607a4de212931373249173e5d20f11fe66bef62

View on Chainz ↗

Height

#298,158

Difficulty

9.991909

Transactions

Size

1.68 KB

Version

Bits

09fdedb8

Nonce

474

Timestamp

12/7/2013, 3:45:03 AM

Confirmations

6,511,327

Mined by

⛏️ aRsAWXYBWKPhGt4UM6JfKUZgx3SbUqQAoisBJ

Merkle Root

b417b65bf43669b18d39404518b328c011aef47afa9e6f5b771d193864bbaf1d

Transactions (4)

Coinbase2f20c49c588085…4fbcb3ae53e1c1

1 in → 26 out10.0000 XPM947 B

AWXYBWKP…qQAoisBJ AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz ASy3AE9X…ghJMwaMJ AJzWx2VD…j4ZSMit5

f1f0b4bfd40639…2186ff4bf21c0e

1 in → 2 out391.4342 XPM226 B

AQntXmsa…iH5Ywv7q ALmAnSnc…6xhjqnbb

25c44c66ab3986…21abfcd857a871

1 in → 2 out390.4178 XPM226 B

AZpX5jFj…ucCGBHXd AVyGxJhW…FgWfSq4s

0120909eb777b2…eed1a8e14732e9

1 in → 2 out389.4057 XPM226 B

AXouRYbt…HZYqnMbm AXcjAJ9k…xEucDG31

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.

4.156 × 10⁹⁶(97-digit number)

41561839209280987625…02202942954635136319

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

4.156 × 10⁹⁶(97-digit number)

41561839209280987625…02202942954635136319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.156 × 10⁹⁶(97-digit number)

41561839209280987625…02202942954635136321

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

8.312 × 10⁹⁶(97-digit number)

83123678418561975250…04405885909270272639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.312 × 10⁹⁶(97-digit number)

83123678418561975250…04405885909270272641

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

1.662 × 10⁹⁷(98-digit number)

16624735683712395050…08811771818540545279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.662 × 10⁹⁷(98-digit number)

16624735683712395050…08811771818540545281

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

3.324 × 10⁹⁷(98-digit number)

33249471367424790100…17623543637081090559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.324 × 10⁹⁷(98-digit number)

33249471367424790100…17623543637081090561

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

6.649 × 10⁹⁷(98-digit number)

66498942734849580200…35247087274162181119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.649 × 10⁹⁷(98-digit number)

66498942734849580200…35247087274162181121

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 #298,158

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