Block #257,748

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 3:45:01 PM · Difficulty 9.9759 · 6,538,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9e26ce8b8b6baa75aaedc0571265bcea84e6e0f7947eac34a2a3694f5968a0f

View on Chainz ↗

Height

#257,748

Difficulty

9.975921

Transactions

Size

2.11 KB

Version

Bits

09f9d5f8

Nonce

7,274

Timestamp

11/12/2013, 3:45:01 PM

Confirmations

6,538,206

Mined by

⛏️ aRMAFwHRcHor7FBYCDWxgtnEzJfYeHAieUvYT

Merkle Root

7cb606680d58545d0adc20a67c416824567462c1625ff0ff88ed950698308d5b

Transactions (1)

Coinbase7cb606680d5854…ed950698308d5b

1 in → 59 out10.0000 XPM2.02 KB

AFwHRcHo…HAieUvYT AFqKfjez…qX9Ace3g ANuKx9Ke…wm7nrBRq 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.

1.023 × 10⁹⁶(97-digit number)

10235053822767162650…11859359242095249859

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

1.023 × 10⁹⁶(97-digit number)

10235053822767162650…11859359242095249859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.023 × 10⁹⁶(97-digit number)

10235053822767162650…11859359242095249861

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

2.047 × 10⁹⁶(97-digit number)

20470107645534325300…23718718484190499719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.047 × 10⁹⁶(97-digit number)

20470107645534325300…23718718484190499721

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

4.094 × 10⁹⁶(97-digit number)

40940215291068650600…47437436968380999439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.094 × 10⁹⁶(97-digit number)

40940215291068650600…47437436968380999441

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

8.188 × 10⁹⁶(97-digit number)

81880430582137301200…94874873936761998879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.188 × 10⁹⁶(97-digit number)

81880430582137301200…94874873936761998881

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

1.637 × 10⁹⁷(98-digit number)

16376086116427460240…89749747873523997759

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