Block #496,388

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 1:55:14 AM · Difficulty 10.7532 · 6,295,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f20d903d0a10c6fa331e50a04ec41873c95cd1d7e71450ce9fd4feb3c825de5

View on Chainz ↗

Height

#496,388

Difficulty

10.753192

Transactions

Size

648 B

Version

Bits

0ac0d12d

Nonce

187,153,828

Timestamp

4/17/2014, 1:55:14 AM

Confirmations

6,295,464

Merkle Root

e806cd8cbcb447f5978cf8ea9ebf20808745d3c1f01daf4ca4006ae59ed2141c

Transactions (2)

Coinbase72a76bffb3624b…77bd1bdec07141

1 in → 1 out8.6400 XPM116 B

AbwWkWZt…kawDhufa

a493d5c30fb9e7…42e541ceae0f42

2 in → 6 out17.5200 XPM441 B

AWQhak32…eArVqMxc AS791b91…2oFChkDv Acd9QzkX…HerMkUNx APRxG4Vc…GZqmXrSs AeKNrjNj…1NEq95Ta

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.

1.218 × 10⁹⁸(99-digit number)

12180117333531963738…61581134094986035839

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

1.218 × 10⁹⁸(99-digit number)

12180117333531963738…61581134094986035839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.218 × 10⁹⁸(99-digit number)

12180117333531963738…61581134094986035841

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

2.436 × 10⁹⁸(99-digit number)

24360234667063927477…23162268189972071679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.436 × 10⁹⁸(99-digit number)

24360234667063927477…23162268189972071681

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

4.872 × 10⁹⁸(99-digit number)

48720469334127854955…46324536379944143359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.872 × 10⁹⁸(99-digit number)

48720469334127854955…46324536379944143361

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

9.744 × 10⁹⁸(99-digit number)

97440938668255709910…92649072759888286719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.744 × 10⁹⁸(99-digit number)

97440938668255709910…92649072759888286721

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

1.948 × 10⁹⁹(100-digit number)

19488187733651141982…85298145519776573439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.948 × 10⁹⁹(100-digit number)

19488187733651141982…85298145519776573441

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