Block #128,350

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/22/2013, 4:18:10 AM · Difficulty 9.7833 · 6,676,617 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

397cd109ba0e1bdc31c9a45491f28de5e8cb4917cca1255779a1fdf21bcd007f

View on Chainz ↗

Height

#128,350

Difficulty

9.783323

Transactions

Size

1.22 KB

Version

Bits

09c887d7

Nonce

181,978

Timestamp

8/22/2013, 4:18:10 AM

Confirmations

6,676,617

Mined by

⛏️ P2SHAbhd9B5foDGSmA1s1oxRxoMfbSPgjPjjv7

Merkle Root

73a9e6b79153573866c1647a1a6b0b7b472070a678d55d78c17f378b0c2a10c2

Transactions (5)

Coinbasef9cb7271211516…472e10887af498

1 in → 1 out10.4700 XPM109 B

Abhd9B5f…PgjPjjv7

211269d778d8ee…fd6af26f0131e8

2 in → 2 out20.9400 XPM372 B

AX7HepGv…Qm28ooHF AKKzWxXf…Jj2dnEGG

084dbbf21eeaa5…bde601db93ea93

1 in → 2 out6.4154 XPM226 B

AK9CYhfA…ZwHcNnPU AVcaTDXp…JjQ2Dxn7

845151f0eac3e0…6a14b318d4cae6

1 in → 2 out2.2209 XPM226 B

AZ3mw5PG…EFsorwgT AHzxAdBT…pXaksKA4

f5fbdbb3290357…60eb60f4a054f6

1 in → 2 out4.2422 XPM227 B

AayHpUDN…zgQkR3A1 AK6DLNgv…M4GgceQx

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.

7.562 × 10⁹⁷(98-digit number)

75620300478098737620…52073864273777925599

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

7.562 × 10⁹⁷(98-digit number)

75620300478098737620…52073864273777925599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.562 × 10⁹⁷(98-digit number)

75620300478098737620…52073864273777925601

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

1.512 × 10⁹⁸(99-digit number)

15124060095619747524…04147728547555851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.512 × 10⁹⁸(99-digit number)

15124060095619747524…04147728547555851201

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

3.024 × 10⁹⁸(99-digit number)

30248120191239495048…08295457095111702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.024 × 10⁹⁸(99-digit number)

30248120191239495048…08295457095111702401

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

6.049 × 10⁹⁸(99-digit number)

60496240382478990096…16590914190223404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.049 × 10⁹⁸(99-digit number)

60496240382478990096…16590914190223404801

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

1.209 × 10⁹⁹(100-digit number)

12099248076495798019…33181828380446809599

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