Block #1,494,603

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2016, 3:35:45 AM · Difficulty 10.6602 · 5,322,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d79706bcd4b489d2f066e74776665914d0bcacf294329da11e837c330ea805c7

View on Chainz ↗

Height

#1,494,603

Difficulty

10.660173

Transactions

Size

3.89 KB

Version

Bits

0aa90120

Nonce

20,781,435

Timestamp

3/13/2016, 3:35:45 AM

Confirmations

5,322,170

Mined by

⛏️ P2SHAVZr4aWpxBZPLF2ujCRoM94PeNhMYaXLXR

Merkle Root

6849fabc5bf6c59b42ecaa11f709a772ef0aaa04cce7b1c0a84b06136f49f5d9

Transactions (3)

Coinbase0e2d903ea0e6f7…da6651de3f1b6a

1 in → 1 out8.8300 XPM110 B

AVZr4aWp…hMYaXLXR

750fa0c0933318…f2ba268e3104ff

1 in → 51 out63.4420 XPM1.85 KB

AMWUhDSb…vws67xkT Ab2y4TAj…Lfu9jYKK AZ3cZHxS…1qdoLqba AWJbVgXA…1LTxX4MP AMiZyJ5m…RED5XPBR

dbb20e0f4eac22…3f21f5fc39ac96

1 in → 51 out15.7816 XPM1.85 KB

AddUSmgB…nsNX1H2E AewX1AUf…GiDrc3EB AHQxW6sN…h3nLA4Aw AFypK4nH…bUiKeJ7y AGwkzXC3…mBQqmTbB

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.

5.848 × 10⁹⁴(95-digit number)

58487675617897024858…95000710047278274239

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

5.848 × 10⁹⁴(95-digit number)

58487675617897024858…95000710047278274239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.848 × 10⁹⁴(95-digit number)

58487675617897024858…95000710047278274241

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

1.169 × 10⁹⁵(96-digit number)

11697535123579404971…90001420094556548479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.169 × 10⁹⁵(96-digit number)

11697535123579404971…90001420094556548481

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

2.339 × 10⁹⁵(96-digit number)

23395070247158809943…80002840189113096959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.339 × 10⁹⁵(96-digit number)

23395070247158809943…80002840189113096961

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

4.679 × 10⁹⁵(96-digit number)

46790140494317619886…60005680378226193919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.679 × 10⁹⁵(96-digit number)

46790140494317619886…60005680378226193921

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

9.358 × 10⁹⁵(96-digit number)

93580280988635239773…20011360756452387839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.358 × 10⁹⁵(96-digit number)

93580280988635239773…20011360756452387841

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 #1,494,603

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