Block #257,904

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 6:14:11 PM · Difficulty 9.9760 · 6,551,861 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36613173d7eaba3eedaaf938692e3b518febc8e285c934685fa5ee647759a8d4

View on Chainz ↗

Height

#257,904

Difficulty

9.975991

Transactions

Size

1.47 KB

Version

Bits

09f9da93

Nonce

32,424

Timestamp

11/12/2013, 6:14:11 PM

Confirmations

6,551,861

Mined by

⛏️ paRnAFqKfjezAQpHxUWGcDetimH5AUqX9Ace3g

Merkle Root

a14beb02afaec486ae03d797ef7236cfeaf911bec43b2f3863aca2598529f408

Transactions (1)

Coinbasea14beb02afaec4…aca2598529f408

1 in → 40 out10.0100 XPM1.39 KB

AFqKfjez…qX9Ace3g AXDu24HR…L9o8sC5D AUtZpWTr…Urwk2Tme AQtzUSwq…htAuF3yC AHeVugNM…1STQZ4jA

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.

2.852 × 10⁹⁰(91-digit number)

28526062335048618028…49212259150037151159

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

2.852 × 10⁹⁰(91-digit number)

28526062335048618028…49212259150037151159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.852 × 10⁹⁰(91-digit number)

28526062335048618028…49212259150037151161

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

5.705 × 10⁹⁰(91-digit number)

57052124670097236057…98424518300074302319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.705 × 10⁹⁰(91-digit number)

57052124670097236057…98424518300074302321

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

1.141 × 10⁹¹(92-digit number)

11410424934019447211…96849036600148604639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.141 × 10⁹¹(92-digit number)

11410424934019447211…96849036600148604641

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

2.282 × 10⁹¹(92-digit number)

22820849868038894423…93698073200297209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.282 × 10⁹¹(92-digit number)

22820849868038894423…93698073200297209281

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

4.564 × 10⁹¹(92-digit number)

45641699736077788846…87396146400594418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.564 × 10⁹¹(92-digit number)

45641699736077788846…87396146400594418561

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

Block #257,904

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