Block #253,392

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 3:07:28 AM · Difficulty 9.9721 · 6,555,282 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f51d73d25842a1bb8fdb26185e3c7d0b6150c21ffdda856fa0ac537ae996cf3

View on Chainz ↗

Height

#253,392

Difficulty

9.972104

Transactions

Size

645 B

Version

Bits

09f8dbcc

Nonce

9,938

Timestamp

11/10/2013, 3:07:28 AM

Confirmations

6,555,282

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

3d058ee67d1881d5ae7d0c44324adaa34c904381156f84bdc806c14af784e1cc

Transactions (3)

Coinbasea6a5784c39b173…18163612293220

1 in → 2 out10.0600 XPM136 B

AZDUEbdS…RYKMRZET ASNt3cJa…L5zCqAYM

6ea8591fa21b61…d8328b295a3bf9

1 in → 1 out9.9971 XPM193 B

AW9FEVK5…L9RUzGJM

18b21acae0403e…362a169a636fd4

1 in → 2 out3.9924 XPM226 B

AbyLdmtS…MKz91xR3 Advr5pAP…YMPi2oT3

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.

2.077 × 10⁹⁵(96-digit number)

20770138849041486839…47277085013951237759

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

2.077 × 10⁹⁵(96-digit number)

20770138849041486839…47277085013951237759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.077 × 10⁹⁵(96-digit number)

20770138849041486839…47277085013951237761

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

4.154 × 10⁹⁵(96-digit number)

41540277698082973678…94554170027902475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.154 × 10⁹⁵(96-digit number)

41540277698082973678…94554170027902475521

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

8.308 × 10⁹⁵(96-digit number)

83080555396165947356…89108340055804951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.308 × 10⁹⁵(96-digit number)

83080555396165947356…89108340055804951041

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

1.661 × 10⁹⁶(97-digit number)

16616111079233189471…78216680111609902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.661 × 10⁹⁶(97-digit number)

16616111079233189471…78216680111609902081

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

3.323 × 10⁹⁶(97-digit number)

33232222158466378942…56433360223219804159

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

Block #253,392

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