Block #476,125

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 3:29:33 PM · Difficulty 10.4690 · 6,326,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

140a70746f5f98a5bbdc686076e8533203d34aa680cadef20ac6fcb697392e65

View on Chainz ↗

Height

#476,125

Difficulty

10.469004

Transactions

Size

937 B

Version

Bits

0a7810a8

Nonce

30,588

Timestamp

4/5/2014, 3:29:33 PM

Confirmations

6,326,417

Mined by

⛏️ CaS@!<YAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c38792b5dfe4cfb19814bf00390ce4ec8657ffdc7ad29502d04ea2d2cc498198

Transactions (1)

Coinbasec38792b5dfe4cf…4ea2d2cc498198

1 in → 23 out9.1100 XPM845 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 Ae2pnFaX…7SPtJMsm 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.

6.013 × 10⁹⁸(99-digit number)

60133622412811764459…45398509184085366079

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

6.013 × 10⁹⁸(99-digit number)

60133622412811764459…45398509184085366079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.013 × 10⁹⁸(99-digit number)

60133622412811764459…45398509184085366081

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

1.202 × 10⁹⁹(100-digit number)

12026724482562352891…90797018368170732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.202 × 10⁹⁹(100-digit number)

12026724482562352891…90797018368170732161

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

2.405 × 10⁹⁹(100-digit number)

24053448965124705783…81594036736341464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.405 × 10⁹⁹(100-digit number)

24053448965124705783…81594036736341464321

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

4.810 × 10⁹⁹(100-digit number)

48106897930249411567…63188073472682928639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.810 × 10⁹⁹(100-digit number)

48106897930249411567…63188073472682928641

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

9.621 × 10⁹⁹(100-digit number)

96213795860498823134…26376146945365857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.621 × 10⁹⁹(100-digit number)

96213795860498823134…26376146945365857281

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