Block #457,954

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 6:36:15 AM · Difficulty 10.4191 · 6,345,553 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1241eef04177663c5fe686f0fbbfedf8eb6adf06610e1dddf3cf9e9840bf64d8

View on Chainz ↗

Height

#457,954

Difficulty

10.419092

Transactions

Size

3.00 KB

Version

Bits

0a6b499a

Nonce

7,950

Timestamp

3/24/2014, 6:36:15 AM

Confirmations

6,345,553

Mined by

⛏️ aSAYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

8ec4f16c8918fcfbe43db39e007f351495e465d7488ee9db284dbe5b6f8173a3

Transactions (4)

Coinbasebe3694645b8cc7…79fef0310e3920

1 in → 1 out9.2000 XPM97 B

AYCeLhqB…eqGM6KK1

6ddb877db3fbea…a9f6a488f7ced7

4 in → 10 out30.1615 XPM840 B

AMWAv1ao…1Drw7eZS AM6M7ug7…EArLB49G AazfaUAJ…WaQjuUwm AeKNrjNj…1NEq95Ta AaaZMezG…Cmtdaf8U

02451bbb54822f…ce38170a9df1db

4 in → 1 out8.2021 XPM636 B

AJcpp52K…bfHKg2T9

470ff7493cc5e6…7312b86efaa287

9 in → 2 out21.5700 XPM1.38 KB

AMBpAAe2…co4xjm2m AHnNDJxn…3TvsDy71

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.

3.847 × 10⁹⁶(97-digit number)

38476047561883914214…06112411988624711679

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

3.847 × 10⁹⁶(97-digit number)

38476047561883914214…06112411988624711679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.847 × 10⁹⁶(97-digit number)

38476047561883914214…06112411988624711681

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

7.695 × 10⁹⁶(97-digit number)

76952095123767828428…12224823977249423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.695 × 10⁹⁶(97-digit number)

76952095123767828428…12224823977249423361

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

1.539 × 10⁹⁷(98-digit number)

15390419024753565685…24449647954498846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.539 × 10⁹⁷(98-digit number)

15390419024753565685…24449647954498846721

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

3.078 × 10⁹⁷(98-digit number)

30780838049507131371…48899295908997693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.078 × 10⁹⁷(98-digit number)

30780838049507131371…48899295908997693441

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

6.156 × 10⁹⁷(98-digit number)

61561676099014262743…97798591817995386879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.156 × 10⁹⁷(98-digit number)

61561676099014262743…97798591817995386881

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