Block #446,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 4:27:22 PM · Difficulty 10.3595 · 6,344,963 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c807a18518220b0df9c2664dbbe8dfbec9e36c9d4891a4a2c68c2c57e8683ed4

View on Chainz ↗

Height

#446,589

Difficulty

10.359523

Transactions

Size

5.95 KB

Version

Bits

0a5c09b9

Nonce

52,170

Timestamp

3/16/2014, 4:27:22 PM

Confirmations

6,344,963

Merkle Root

fd8ace505f800638adcff2564dd028d388b228c7002dae636f88f7e3cfed5ae1

Transactions (4)

Coinbase70ff044af96ae7…c48bab8eae50b2

1 in → 1 out9.3800 XPM109 B

Ae6V4Kr2…Fr3rRnk5

3a4948dee9cce1…e662c71836c19d

1 in → 4 out9.3200 XPM261 B

Aai7rmvE…JWhtS5Q5 AeKNrjNj…1NEq95Ta AesAVNRf…eAXARtnF AZPfcp6j…3BCLLL8o

f6c2c237cbe7b2…09838f9c3ed865

1 in → 2 out300.0800 XPM227 B

Ae1jDD8j…9tCJ9dqz AeHJ4ewv…ijr7F28o

fbda50cef50d82…a7d3f025934f58

36 in → 2 out12.0704 XPM5.28 KB

AGwg6tEm…Fsz3FW5B ARmWB4u6…iZXCL88p

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.

4.509 × 10⁹⁴(95-digit number)

45098862574531176281…33294131316827438879

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

4.509 × 10⁹⁴(95-digit number)

45098862574531176281…33294131316827438879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.509 × 10⁹⁴(95-digit number)

45098862574531176281…33294131316827438881

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

9.019 × 10⁹⁴(95-digit number)

90197725149062352563…66588262633654877759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.019 × 10⁹⁴(95-digit number)

90197725149062352563…66588262633654877761

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

1.803 × 10⁹⁵(96-digit number)

18039545029812470512…33176525267309755519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.803 × 10⁹⁵(96-digit number)

18039545029812470512…33176525267309755521

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

3.607 × 10⁹⁵(96-digit number)

36079090059624941025…66353050534619511039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.607 × 10⁹⁵(96-digit number)

36079090059624941025…66353050534619511041

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

7.215 × 10⁹⁵(96-digit number)

72158180119249882050…32706101069239022079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.215 × 10⁹⁵(96-digit number)

72158180119249882050…32706101069239022081

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