Block #248,969

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 4:46:39 PM · Difficulty 9.9663 · 6,554,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c43161f4e03d6cbba13bd42f8f21e8252a1622aa0ee15ecbc4ee233a3b31462

View on Chainz ↗

Height

#248,969

Difficulty

9.966339

Transactions

Size

2.07 KB

Version

Bits

09f761f8

Nonce

167

Timestamp

11/7/2013, 4:46:39 PM

Confirmations

6,554,918

Mined by

⛏️ R{AQDGVS66x4YUbhY3Z3fTFJcuAE1PTWdWkm

Merkle Root

2b1532736d3cf3f607f7b73cbb53bbcd34c86704f45183c7042e274adb342e81

Transactions (1)

Coinbase2b1532736d3cf3…2e274adb342e81

1 in → 58 out10.0200 XPM1.99 KB

AQDGVS66…1PTWdWkm ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AJKYzp1g…SvZiepke AMbCuLHZ…WSoStwkc

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.

1.594 × 10⁹³(94-digit number)

15942247457471663705…51155196375447516639

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

1.594 × 10⁹³(94-digit number)

15942247457471663705…51155196375447516639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.594 × 10⁹³(94-digit number)

15942247457471663705…51155196375447516641

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

3.188 × 10⁹³(94-digit number)

31884494914943327411…02310392750895033279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.188 × 10⁹³(94-digit number)

31884494914943327411…02310392750895033281

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

6.376 × 10⁹³(94-digit number)

63768989829886654822…04620785501790066559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.376 × 10⁹³(94-digit number)

63768989829886654822…04620785501790066561

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

1.275 × 10⁹⁴(95-digit number)

12753797965977330964…09241571003580133119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.275 × 10⁹⁴(95-digit number)

12753797965977330964…09241571003580133121

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

2.550 × 10⁹⁴(95-digit number)

25507595931954661928…18483142007160266239

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