Block #150,396

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 12:07:08 AM · Difficulty 9.8589 · 6,652,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48f26104250c19070873672ead21a66ad271bc0f396fd6ad58711a7da9caedb2

View on Chainz ↗

Height

#150,396

Difficulty

9.858941

Transactions

Size

1017 B

Version

Bits

09dbe389

Nonce

30,016

Timestamp

9/5/2013, 12:07:08 AM

Confirmations

6,652,061

Mined by

⛏️ P2SHAPEcDKBhiwmtCs4uPmnx1PYtaBbvmts2ty

Merkle Root

13b8863b4ac05c6bf561c1a6b013fc92deae14bafce6d84bb72084155d2c5795

Transactions (2)

Coinbase936243c4d843bd…b8f639941e5402

1 in → 1 out10.2800 XPM109 B

APEcDKBh…bvmts2ty

46f914f062d603…4e806d66cc44e3

5 in → 2 out25.0783 XPM820 B

AVbUYygu…86BSkU3f AcUoX8DT…EGfZnDUq

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.

3.096 × 10⁹⁰(91-digit number)

30962881167879339718…31500451835178864219

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

3.096 × 10⁹⁰(91-digit number)

30962881167879339718…31500451835178864219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.096 × 10⁹⁰(91-digit number)

30962881167879339718…31500451835178864221

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

6.192 × 10⁹⁰(91-digit number)

61925762335758679436…63000903670357728439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.192 × 10⁹⁰(91-digit number)

61925762335758679436…63000903670357728441

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

1.238 × 10⁹¹(92-digit number)

12385152467151735887…26001807340715456879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10⁹¹(92-digit number)

12385152467151735887…26001807340715456881

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

2.477 × 10⁹¹(92-digit number)

24770304934303471774…52003614681430913759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.477 × 10⁹¹(92-digit number)

24770304934303471774…52003614681430913761

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

4.954 × 10⁹¹(92-digit number)

49540609868606943549…04007229362861827519

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