Block #456,619

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 8:33:08 AM · Difficulty 10.4174 · 6,350,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42e4b1e485d733d600b76fb8e1d3de86a5e5676e817cd61df6895f41578edf05

View on Chainz ↗

Height

#456,619

Difficulty

10.417443

Transactions

Size

902 B

Version

Bits

0a6add89

Nonce

111,641

Timestamp

3/23/2014, 8:33:08 AM

Confirmations

6,350,074

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

88ab15b37d44196c100d8d1a39369cc966980312fbe3c9953fc256969c61e1c0

Transactions (1)

Coinbase88ab15b37d4419…c256969c61e1c0

1 in → 22 out9.2000 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AH5mD99t…Spv1yg4N AZr7Ptuw…CM4Yw5jq AUzEPJFG…kYkA5U9V

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.

1.712 × 10⁹⁸(99-digit number)

17123463414619175401…91136839014926110079

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

1.712 × 10⁹⁸(99-digit number)

17123463414619175401…91136839014926110079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.712 × 10⁹⁸(99-digit number)

17123463414619175401…91136839014926110081

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

3.424 × 10⁹⁸(99-digit number)

34246926829238350802…82273678029852220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.424 × 10⁹⁸(99-digit number)

34246926829238350802…82273678029852220161

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

6.849 × 10⁹⁸(99-digit number)

68493853658476701604…64547356059704440319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.849 × 10⁹⁸(99-digit number)

68493853658476701604…64547356059704440321

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

1.369 × 10⁹⁹(100-digit number)

13698770731695340320…29094712119408880639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.369 × 10⁹⁹(100-digit number)

13698770731695340320…29094712119408880641

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

2.739 × 10⁹⁹(100-digit number)

27397541463390680641…58189424238817761279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.739 × 10⁹⁹(100-digit number)

27397541463390680641…58189424238817761281

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

Block #456,619

Cookie Preferences