Block #151,428

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 4:30:29 PM · Difficulty 9.8603 · 6,654,569 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3306058f04b65b807cdd8d14e0a1b4bffc0b681eb25ef62dc01b9ceadf653c9

View on Chainz ↗

Height

#151,428

Difficulty

9.860342

Transactions

Size

391 B

Version

Bits

09dc3f5d

Nonce

43,833

Timestamp

9/5/2013, 4:30:29 PM

Confirmations

6,654,569

Mined by

⛏️ P2SHAJkcBGvuouoWiEQ4AmFvGo3qwPhSNwhPED

Merkle Root

46f2308961202afe609e6269292b7b2a787b016f621bd2f533c7e26d3bbbbf85

Transactions (2)

Coinbase4691e3798ae6a9…aa605b0f46bfe0

1 in → 1 out10.2800 XPM109 B

AJkcBGvu…hSNwhPED

d106ae72772403…549f7e48b786d9

1 in → 2 out10.2700 XPM192 B

AFz9fXym…wh4UqpkL AdT5PbaZ…tc7AWv8M

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.

6.939 × 10⁹³(94-digit number)

69394045818190642853…20172800186565153979

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

6.939 × 10⁹³(94-digit number)

69394045818190642853…20172800186565153979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.939 × 10⁹³(94-digit number)

69394045818190642853…20172800186565153981

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

1.387 × 10⁹⁴(95-digit number)

13878809163638128570…40345600373130307959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.387 × 10⁹⁴(95-digit number)

13878809163638128570…40345600373130307961

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

2.775 × 10⁹⁴(95-digit number)

27757618327276257141…80691200746260615919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.775 × 10⁹⁴(95-digit number)

27757618327276257141…80691200746260615921

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

5.551 × 10⁹⁴(95-digit number)

55515236654552514282…61382401492521231839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.551 × 10⁹⁴(95-digit number)

55515236654552514282…61382401492521231841

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

1.110 × 10⁹⁵(96-digit number)

11103047330910502856…22764802985042463679

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