Block #149,428

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 9:02:23 AM · Difficulty 9.8571 · 6,659,438 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17cf16a62c7a25d9c1b90e5f53e0f1a51f7c9903d0e59bc0af8464d5aa046bc5

View on Chainz ↗

Height

#149,428

Difficulty

9.857138

Transactions

Size

7.50 KB

Version

Bits

09db6d62

Nonce

97,200

Timestamp

9/4/2013, 9:02:23 AM

Confirmations

6,659,438

Mined by

⛏️ P2SHAbhLnFav9ZKbs4sn9gYHWQLdXRzwSfJm9T

Merkle Root

d9abde1b7a2afd31dc4258639f25180aefc32f6a804781de72ba26bc19b2279a

Transactions (2)

Coinbase63559fc8c431a9…afd3593d998591

1 in → 1 out10.3900 XPM109 B

AbhLnFav…zwSfJm9T

f6ffc95a622258…c6c3c0853b7cef

50 in → 2 out10000.0101 XPM7.30 KB

AaBz9wfQ…Kds8Xfa5 AS6m9c8d…7KWnbnjY

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.

1.309 × 10⁹⁶(97-digit number)

13099992229598237664…07353398194465964239

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

1.309 × 10⁹⁶(97-digit number)

13099992229598237664…07353398194465964239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.309 × 10⁹⁶(97-digit number)

13099992229598237664…07353398194465964241

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

2.619 × 10⁹⁶(97-digit number)

26199984459196475329…14706796388931928479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.619 × 10⁹⁶(97-digit number)

26199984459196475329…14706796388931928481

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

5.239 × 10⁹⁶(97-digit number)

52399968918392950658…29413592777863856959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.239 × 10⁹⁶(97-digit number)

52399968918392950658…29413592777863856961

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

1.047 × 10⁹⁷(98-digit number)

10479993783678590131…58827185555727713919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.047 × 10⁹⁷(98-digit number)

10479993783678590131…58827185555727713921

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

2.095 × 10⁹⁷(98-digit number)

20959987567357180263…17654371111455427839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #149,428

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