Block #454,124

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 5:46:40 PM · Difficulty 10.3953 · 6,341,509 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7aae8fb1e4d7849ab55a62c26aee9b3b87594035ac1174d80c5b801f340791e0

View on Chainz ↗

Height

#454,124

Difficulty

10.395299

Transactions

Size

1.08 KB

Version

Bits

0a65324f

Nonce

19,695

Timestamp

3/21/2014, 5:46:40 PM

Confirmations

6,341,509

Mined by

⛏️ P2SHAJvVGNDrrMGkCtaY7BDwYm2d7rS1xoZfnU

Merkle Root

07f547f521f60504052d27e42a9fbf368c98b2ff088a474f34ac7cf0f08d3e0d

Transactions (5)

Coinbase59d528744fd869…cd731fc34090c2

1 in → 1 out9.2800 XPM110 B

AJvVGNDr…S1xoZfnU

23571b2bf894bf…83712b287a877d

1 in → 2 out7.2021 XPM225 B

AWoUABSP…5d8C6XMp AZMs6PQy…hxKsRcgB

3bd50425853237…ea71e55916ed39

1 in → 2 out5.1780 XPM226 B

AavM9ADQ…s5wFV2jY AWTSEZwE…JM5KKNMF

d773a788f35346…f4cd9ec25f85c7

1 in → 2 out3.1865 XPM226 B

ASfQj9Pb…Q87HBF2g AQ5U5zB5…q7D4oXya

80dff1159e4da0…858ebab1a9b5f0

1 in → 2 out2.3341 XPM226 B

AcP8jseU…hwvN422m AYKozZax…5vQ5myok

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.

1.538 × 10⁹⁸(99-digit number)

15384726802124242836…34097106937443174399

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

1.538 × 10⁹⁸(99-digit number)

15384726802124242836…34097106937443174399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.538 × 10⁹⁸(99-digit number)

15384726802124242836…34097106937443174401

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

3.076 × 10⁹⁸(99-digit number)

30769453604248485673…68194213874886348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.076 × 10⁹⁸(99-digit number)

30769453604248485673…68194213874886348801

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

6.153 × 10⁹⁸(99-digit number)

61538907208496971346…36388427749772697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.153 × 10⁹⁸(99-digit number)

61538907208496971346…36388427749772697601

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

1.230 × 10⁹⁹(100-digit number)

12307781441699394269…72776855499545395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.230 × 10⁹⁹(100-digit number)

12307781441699394269…72776855499545395201

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

2.461 × 10⁹⁹(100-digit number)

24615562883398788538…45553710999090790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.461 × 10⁹⁹(100-digit number)

24615562883398788538…45553710999090790401

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