Block #49,645

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 9:23:48 PM · Difficulty 8.8688 · 6,740,103 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a10c1e711721f51dc49c2c897ff371218ac210a9dfff8c89f0f8c26a0002be28

View on Chainz ↗

Height

#49,645

Difficulty

8.868767

Transactions

Size

767 B

Version

Bits

08de6783

Nonce

184

Timestamp

7/15/2013, 9:23:48 PM

Confirmations

6,740,103

Merkle Root

5c2a5cc151a27f00fbffb86e800cd0c2fc1ba6642170f2f51254e41b46ee45ff

Transactions (2)

Coinbase406a9932cf7786…103c0a1b8aacb3

1 in → 1 out12.7100 XPM110 B

AHgLH46H…EzxMwQkm

73088a8bd5be1a…cc7e544780a70b

4 in → 1 out38.1550 XPM567 B

AL5iHwkH…YGkGxDZC

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.

2.428 × 10⁹⁴(95-digit number)

24281212090991434805…67093618744853884459

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

2.428 × 10⁹⁴(95-digit number)

24281212090991434805…67093618744853884459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.428 × 10⁹⁴(95-digit number)

24281212090991434805…67093618744853884461

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

4.856 × 10⁹⁴(95-digit number)

48562424181982869610…34187237489707768919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.856 × 10⁹⁴(95-digit number)

48562424181982869610…34187237489707768921

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

9.712 × 10⁹⁴(95-digit number)

97124848363965739221…68374474979415537839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.712 × 10⁹⁴(95-digit number)

97124848363965739221…68374474979415537841

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

1.942 × 10⁹⁵(96-digit number)

19424969672793147844…36748949958831075679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.942 × 10⁹⁵(96-digit number)

19424969672793147844…36748949958831075681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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