Block #596,792

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2014, 9:59:57 AM · Difficulty 10.9340 · 6,217,400 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb88f89e892666b08b195f14676223af2fc936fb3f6cc7afd60e818740dafe59

View on Chainz ↗

Height

#596,792

Difficulty

10.933969

Transactions

Size

1.37 KB

Version

Bits

0aef189e

Nonce

41,353,047

Timestamp

6/21/2014, 9:59:57 AM

Confirmations

6,217,400

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e3566b08f71bfe404b3cbcfb6bfcef0e40f29d51b825090430a07ae7fb174528

Transactions (3)

Coinbase6452f7026e8a22…5ae6c7e7d65b7a

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

4d771fcefc206d…a171aaeb45d2c3

1 in → 2 out1.7391 XPM226 B

APnzp8Nq…mNK8qwg3 AS9ZCvju…bu3NEFwZ

9be37e7e0cda2a…ebf4f2c225b44c

6 in → 2 out1.0101 XPM967 B

AVsFJoju…q9e9rkcJ AdTMZTDU…gWcJoiUq

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.

5.128 × 10⁹⁷(98-digit number)

51282010766940833761…46503803033137230959

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

5.128 × 10⁹⁷(98-digit number)

51282010766940833761…46503803033137230959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.128 × 10⁹⁷(98-digit number)

51282010766940833761…46503803033137230961

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

1.025 × 10⁹⁸(99-digit number)

10256402153388166752…93007606066274461919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.025 × 10⁹⁸(99-digit number)

10256402153388166752…93007606066274461921

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

2.051 × 10⁹⁸(99-digit number)

20512804306776333504…86015212132548923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.051 × 10⁹⁸(99-digit number)

20512804306776333504…86015212132548923841

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

4.102 × 10⁹⁸(99-digit number)

41025608613552667009…72030424265097847679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.102 × 10⁹⁸(99-digit number)

41025608613552667009…72030424265097847681

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

8.205 × 10⁹⁸(99-digit number)

82051217227105334018…44060848530195695359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.205 × 10⁹⁸(99-digit number)

82051217227105334018…44060848530195695361

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 #596,792

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