Block #301,967

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 1:18:25 PM · Difficulty 9.9926 · 6,507,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e79c03e5901e38c2556ebf1c9efa01973d1b295c5e98f371705005babf942c50

View on Chainz ↗

Height

#301,967

Difficulty

9.992576

Transactions

Size

799 B

Version

Bits

09fe197e

Nonce

1,370

Timestamp

12/9/2013, 1:18:25 PM

Confirmations

6,507,507

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0ae5e40b827ecc343e2fcc8ec94584327f51e452f18ff37858281a922560b906

Transactions (3)

Coinbase7d1597e526516f…dbae82d387c972

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

cfb072cddd16a4…4b6ede499be996

2 in → 2 out3.1887 XPM373 B

ANGMWihR…LKRCHYRP AV4qKi25…bZARP8Xi

baca152fba13c5…33a7b61488ad35

1 in → 2 out2.6949 XPM226 B

AKfarav5…u94Lynoi AJz987nj…X2bMmzq6

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.

4.145 × 10⁹⁴(95-digit number)

41452286344614640268…80063420423673221119

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

4.145 × 10⁹⁴(95-digit number)

41452286344614640268…80063420423673221119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.145 × 10⁹⁴(95-digit number)

41452286344614640268…80063420423673221121

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

8.290 × 10⁹⁴(95-digit number)

82904572689229280536…60126840847346442239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.290 × 10⁹⁴(95-digit number)

82904572689229280536…60126840847346442241

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

1.658 × 10⁹⁵(96-digit number)

16580914537845856107…20253681694692884479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.658 × 10⁹⁵(96-digit number)

16580914537845856107…20253681694692884481

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

3.316 × 10⁹⁵(96-digit number)

33161829075691712214…40507363389385768959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.316 × 10⁹⁵(96-digit number)

33161829075691712214…40507363389385768961

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

6.632 × 10⁹⁵(96-digit number)

66323658151383424429…81014726778771537919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.632 × 10⁹⁵(96-digit number)

66323658151383424429…81014726778771537921

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 #301,967

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