Block #51,489

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 6:00:46 AM · Difficulty 8.8992 · 6,758,313 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c626410febed7eeddcc01ac0d7aba52fe3c6dca3de4a66d3b4adf13de9376f4d

View on Chainz ↗

Height

#51,489

Difficulty

8.899199

Transactions

Size

428 B

Version

Bits

08e631ea

Nonce

274

Timestamp

7/16/2013, 6:00:46 AM

Confirmations

6,758,313

Mined by

⛏️ P2SHAYUtU1Te4yz9iT5mceYdSV6DxTF473AgyP

Merkle Root

6d1f404be038c9f7f80098987625993b9c37370481687fc9e52a70190d040c20

Transactions (2)

Coinbased7cc008ce3e963…b853adb223391e

1 in → 1 out12.6200 XPM110 B

AYUtU1Te…F473AgyP

f0a9e2e81f11f4…cadc6d618603b4

1 in → 2 out2407.9600 XPM225 B

APE1dWFB…3PrGLeMk AVNqMZi5…iq8px3w9

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.

7.945 × 10¹⁰¹(102-digit number)

79451001648546062654…97509878982412135399

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

7.945 × 10¹⁰¹(102-digit number)

79451001648546062654…97509878982412135399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.945 × 10¹⁰¹(102-digit number)

79451001648546062654…97509878982412135401

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

1.589 × 10¹⁰²(103-digit number)

15890200329709212530…95019757964824270799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.589 × 10¹⁰²(103-digit number)

15890200329709212530…95019757964824270801

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

3.178 × 10¹⁰²(103-digit number)

31780400659418425061…90039515929648541599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.178 × 10¹⁰²(103-digit number)

31780400659418425061…90039515929648541601

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

6.356 × 10¹⁰²(103-digit number)

63560801318836850123…80079031859297083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.356 × 10¹⁰²(103-digit number)

63560801318836850123…80079031859297083201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #51,489

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