Block #255,123

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 2:47:39 AM · Difficulty 9.9738 · 6,534,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5a3eee99ac7eade00af53ded00a3a26f3e696067810bd245d34e29441d0314a

View on Chainz ↗

Height

#255,123

Difficulty

9.973827

Transactions

Size

836 B

Version

Bits

09f94cbc

Nonce

18,209

Timestamp

11/11/2013, 2:47:39 AM

Confirmations

6,534,770

Merkle Root

41bee52068d281ffc6e8d514582b0e7503270d487d545663e2ca241bdd15a023

Transactions (4)

Coinbase7c50cbc7246041…f97ece90de568e

1 in → 2 out10.0700 XPM137 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

1a0a87468531e3…e56e139074e704

1 in → 1 out10.1600 XPM157 B

AbF7taLP…caPQgpyF

57f81dce51ac1e…98b832a56f1e67

1 in → 2 out6.6061 XPM226 B

AHTtZLtW…gDhZFjpM ATrXGf54…Ny27xZZ9

9b42c136f5dcae…82233fddc5f13d

1 in → 2 out5.9568 XPM226 B

AMmGeXac…8N1iWEtv AJQbPwc4…w4nzRJwM

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.

4.401 × 10⁹⁴(95-digit number)

44010157277134466993…26230132203970510159

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

4.401 × 10⁹⁴(95-digit number)

44010157277134466993…26230132203970510159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.401 × 10⁹⁴(95-digit number)

44010157277134466993…26230132203970510161

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

8.802 × 10⁹⁴(95-digit number)

88020314554268933987…52460264407941020319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.802 × 10⁹⁴(95-digit number)

88020314554268933987…52460264407941020321

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

1.760 × 10⁹⁵(96-digit number)

17604062910853786797…04920528815882040639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.760 × 10⁹⁵(96-digit number)

17604062910853786797…04920528815882040641

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

3.520 × 10⁹⁵(96-digit number)

35208125821707573594…09841057631764081279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.520 × 10⁹⁵(96-digit number)

35208125821707573594…09841057631764081281

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

7.041 × 10⁹⁵(96-digit number)

70416251643415147189…19682115263528162559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.041 × 10⁹⁵(96-digit number)

70416251643415147189…19682115263528162561

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