Block #149,952

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 5:14:14 PM · Difficulty 9.8580 · 6,660,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

afe129741c9d3e24e18db7610f2fe196c1f5795381769b541416b1fbb2b245cf

View on Chainz ↗

Height

#149,952

Difficulty

9.858041

Transactions

Size

721 B

Version

Bits

09dba890

Nonce

17,785

Timestamp

9/4/2013, 5:14:14 PM

Confirmations

6,660,308

Mined by

⛏️ P2SHAdG7QfDy9FHKcJNFSY8neccEaaTW63iqGP

Merkle Root

eceb589a26d31ab1da630e71fd0c043669f0a9f5183da28bbf34cb2667a7d889

Transactions (2)

Coinbase80bca79a06f058…ec0285eb87a09b

1 in → 1 out10.2800 XPM109 B

AdG7QfDy…TW63iqGP

b905882c1270b4…dd647261dc0802

3 in → 2 out317.9233 XPM523 B

AWEbEkW9…HuaEB7tB Ab7iXvjf…LnFwMDZn

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.

6.786 × 10⁹¹(92-digit number)

67863689647672854257…25859868119472569239

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

6.786 × 10⁹¹(92-digit number)

67863689647672854257…25859868119472569239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.786 × 10⁹¹(92-digit number)

67863689647672854257…25859868119472569241

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

1.357 × 10⁹²(93-digit number)

13572737929534570851…51719736238945138479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.357 × 10⁹²(93-digit number)

13572737929534570851…51719736238945138481

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

2.714 × 10⁹²(93-digit number)

27145475859069141702…03439472477890276959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.714 × 10⁹²(93-digit number)

27145475859069141702…03439472477890276961

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

5.429 × 10⁹²(93-digit number)

54290951718138283405…06878944955780553919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.429 × 10⁹²(93-digit number)

54290951718138283405…06878944955780553921

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

1.085 × 10⁹³(94-digit number)

10858190343627656681…13757889911561107839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.085 × 10⁹³(94-digit number)

10858190343627656681…13757889911561107841

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 #149,952

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