Block #310,450

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 2:01:52 AM · Difficulty 9.9952 · 6,500,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95330f99a60d952c79893e4497c3d70cc50e4af0888319ce166c2138d0d4edf2

View on Chainz ↗

Height

#310,450

Difficulty

9.995187

Transactions

Size

1.57 KB

Version

Bits

09fec496

Nonce

2,294

Timestamp

12/14/2013, 2:01:52 AM

Confirmations

6,500,403

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

e76a8388cfe597762abadbf5e3c182dc3bc17edfa77d11ddb9ebe5a2bf5ea435

Transactions (2)

Coinbase1533129c2e5039…103c89f751752f

1 in → 23 out9.9900 XPM845 B

Aac9Hjdg…P4ktypc3 AbHskoSG…cKTUEpAH ATiP2myP…qVUH8Grb ARcqMJhp…RVLToQ6S AbtgNzNb…9Atvu81w

28eed19cdcc90e…ed91b3695c0267

4 in → 2 out0.6178 XPM669 B

AMNCkQXM…vnA6Pobt AGe6a47X…AVCnAXX1

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.

1.577 × 10⁹⁵(96-digit number)

15772139779096377201…87123965818958394999

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

1.577 × 10⁹⁵(96-digit number)

15772139779096377201…87123965818958394999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.577 × 10⁹⁵(96-digit number)

15772139779096377201…87123965818958395001

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

3.154 × 10⁹⁵(96-digit number)

31544279558192754402…74247931637916789999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.154 × 10⁹⁵(96-digit number)

31544279558192754402…74247931637916790001

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

6.308 × 10⁹⁵(96-digit number)

63088559116385508804…48495863275833579999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.308 × 10⁹⁵(96-digit number)

63088559116385508804…48495863275833580001

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

1.261 × 10⁹⁶(97-digit number)

12617711823277101760…96991726551667159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.261 × 10⁹⁶(97-digit number)

12617711823277101760…96991726551667160001

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

2.523 × 10⁹⁶(97-digit number)

25235423646554203521…93983453103334319999

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 #310,450

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