Block #462,769

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 4:02:58 PM · Difficulty 10.4145 · 6,332,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fdeb334516a764efef69f16661a604372c9832a173614113fdbbe31676795f9

View on Chainz ↗

Height

#462,769

Difficulty

10.414475

Transactions

Size

1.62 KB

Version

Bits

0a6a1b10

Nonce

217,963

Timestamp

3/27/2014, 4:02:58 PM

Confirmations

6,332,517

Mined by

⛏️ aS4KTATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

427a86ed7dcfa435c87c794f0757a78cfe77ce81cc80a29433b4a5b2d7f66009

Transactions (4)

Coinbase95394db4892dbb…0c0d33e1454ced

1 in → 20 out9.2100 XPM743 B

ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ AJtNW28X…Syb4Ph5j Ac7TsAMG…2W5MRTA8 AVjRurTS…6rE1YXsF

cb873fe0f5e7ab…c3860a688c6a84

2 in → 2 out15.0820 XPM372 B

AJnTo2uV…LyQfNRpb AdjnVxys…cw3ByVS5

46c4c9a4917141…ac99878fe3f441

1 in → 2 out5.5968 XPM226 B

ANWMxvTy…X3aR6WDK AT3ySxdP…BMy2CorU

00f2d7f420350f…78b327670bb064

1 in → 2 out5.1222 XPM225 B

APFsQ3Fo…xoFKrF12 AKyeTgmJ…iCQ5jKFP

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.

3.038 × 10⁹⁴(95-digit number)

30384940238462252438…48203215883397023579

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

3.038 × 10⁹⁴(95-digit number)

30384940238462252438…48203215883397023579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.038 × 10⁹⁴(95-digit number)

30384940238462252438…48203215883397023581

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

6.076 × 10⁹⁴(95-digit number)

60769880476924504877…96406431766794047159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.076 × 10⁹⁴(95-digit number)

60769880476924504877…96406431766794047161

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

1.215 × 10⁹⁵(96-digit number)

12153976095384900975…92812863533588094319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.215 × 10⁹⁵(96-digit number)

12153976095384900975…92812863533588094321

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

2.430 × 10⁹⁵(96-digit number)

24307952190769801950…85625727067176188639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.430 × 10⁹⁵(96-digit number)

24307952190769801950…85625727067176188641

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

4.861 × 10⁹⁵(96-digit number)

48615904381539603901…71251454134352377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.861 × 10⁹⁵(96-digit number)

48615904381539603901…71251454134352377281

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