Block #159,785

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 10:01:00 AM · Difficulty 9.8636 · 6,649,027 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91f151244df5f204989de85a3ddab2ecfd68a5de271ef2514b776831310ac97a

View on Chainz ↗

Height

#159,785

Difficulty

9.863555

Transactions

Size

889 B

Version

Bits

09dd11f0

Nonce

105,121

Timestamp

9/11/2013, 10:01:00 AM

Confirmations

6,649,027

Mined by

⛏️ P2SHAXJjtfzhefWfb3eA5KccL8yQLL3gEJ6kbP

Merkle Root

d0bb814cf2edda8d1d993cef409685fb02e78e5272ef7f985356dfc10439840a

Transactions (3)

Coinbase247754ed0e8c1c…9177c91ac463d4

1 in → 1 out10.2800 XPM109 B

AXJjtfzh…3gEJ6kbP

7396cdd4c450ff…6f824a59ec52ca

4 in → 1 out41.0100 XPM499 B

AbxSykSg…BX71twYi

3ac6f4092a38d2…cae904d6f295b0

1 in → 2 out10.2400 XPM191 B

AZf3Ymwe…aUpMz8nU AFz9fXym…wh4UqpkL

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.

1.449 × 10⁹⁴(95-digit number)

14493149376675066114…12529144491875775999

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

1.449 × 10⁹⁴(95-digit number)

14493149376675066114…12529144491875775999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.449 × 10⁹⁴(95-digit number)

14493149376675066114…12529144491875776001

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

2.898 × 10⁹⁴(95-digit number)

28986298753350132229…25058288983751551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.898 × 10⁹⁴(95-digit number)

28986298753350132229…25058288983751552001

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

5.797 × 10⁹⁴(95-digit number)

57972597506700264458…50116577967503103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.797 × 10⁹⁴(95-digit number)

57972597506700264458…50116577967503104001

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

1.159 × 10⁹⁵(96-digit number)

11594519501340052891…00233155935006207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.159 × 10⁹⁵(96-digit number)

11594519501340052891…00233155935006208001

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

2.318 × 10⁹⁵(96-digit number)

23189039002680105783…00466311870012415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.318 × 10⁹⁵(96-digit number)

23189039002680105783…00466311870012416001

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 #159,785

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