Block #945,469

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/21/2015, 3:42:27 AM · Difficulty 10.8987 · 5,871,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75c4f61c5cbbe647da3940142365d9eba2cca33c1c2f29ced00039d9c76ec31d

View on Chainz ↗

Height

#945,469

Difficulty

10.898671

Transactions

Size

1.51 KB

Version

Bits

0ae60f55

Nonce

56,741,090

Timestamp

2/21/2015, 3:42:27 AM

Confirmations

5,871,482

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f1c94d6a602099a4cccfa27cd0123b868304be2462aee56c708fe352ea258781

Transactions (3)

Coinbaseb2bffff0b36700…9103d2f2cfcead

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

53a14c640e4ff7…fc1c571be9a7f0

7 in → 2 out20.1393 XPM1.09 KB

ARyCUdFz…iAG4hb9n AUe9RUaD…ZbZ1ev3j

04b906f8633650…934a827283efa8

1 in → 2 out2.5697 XPM225 B

AZaP8Jpw…37x6Ao45 AVhxFrw7…RKtfVTWF

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.

1.541 × 10⁹⁶(97-digit number)

15412520418204276834…28349006018444472799

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

1.541 × 10⁹⁶(97-digit number)

15412520418204276834…28349006018444472799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.541 × 10⁹⁶(97-digit number)

15412520418204276834…28349006018444472801

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

3.082 × 10⁹⁶(97-digit number)

30825040836408553668…56698012036888945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.082 × 10⁹⁶(97-digit number)

30825040836408553668…56698012036888945601

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

6.165 × 10⁹⁶(97-digit number)

61650081672817107336…13396024073777891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.165 × 10⁹⁶(97-digit number)

61650081672817107336…13396024073777891201

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

1.233 × 10⁹⁷(98-digit number)

12330016334563421467…26792048147555782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.233 × 10⁹⁷(98-digit number)

12330016334563421467…26792048147555782401

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

2.466 × 10⁹⁷(98-digit number)

24660032669126842934…53584096295111564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.466 × 10⁹⁷(98-digit number)

24660032669126842934…53584096295111564801

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 #945,469

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