Block #462,653

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 1:59:58 PM · Difficulty 10.4153 · 6,336,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d341c4e429f140d2a8d36edbadf5975e62879123e9e879f218ac4cc8bdb3bf43

View on Chainz ↗

Height

#462,653

Difficulty

10.415261

Transactions

Size

968 B

Version

Bits

0a6a4e8f

Nonce

89,661

Timestamp

3/27/2014, 1:59:58 PM

Confirmations

6,336,555

Mined by

⛏️ =aS4.rAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0c28a8dd9ae268e3cd47726bba287e568bb56925cd9cd9467a48f33a0aa446f1

Transactions (1)

Coinbase0c28a8dd9ae268…48f33a0aa446f1

1 in → 24 out9.2000 XPM879 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

5.047 × 10⁹²(93-digit number)

50471521841414853293…65017730677733554719

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

5.047 × 10⁹²(93-digit number)

50471521841414853293…65017730677733554719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.047 × 10⁹²(93-digit number)

50471521841414853293…65017730677733554721

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

1.009 × 10⁹³(94-digit number)

10094304368282970658…30035461355467109439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.009 × 10⁹³(94-digit number)

10094304368282970658…30035461355467109441

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

2.018 × 10⁹³(94-digit number)

20188608736565941317…60070922710934218879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.018 × 10⁹³(94-digit number)

20188608736565941317…60070922710934218881

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

4.037 × 10⁹³(94-digit number)

40377217473131882634…20141845421868437759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.037 × 10⁹³(94-digit number)

40377217473131882634…20141845421868437761

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

8.075 × 10⁹³(94-digit number)

80754434946263765269…40283690843736875519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.075 × 10⁹³(94-digit number)

80754434946263765269…40283690843736875521

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