Block #497,227

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 11:57:16 AM · Difficulty 10.7647 · 6,316,639 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67a7bcf7447a7de3aac505b4575520ad373fe4a1b09cce1da9a1e7cc8b9d6715

View on Chainz ↗

Height

#497,227

Difficulty

10.764664

Transactions

Size

1.35 KB

Version

Bits

0ac3c10a

Nonce

167,545,819

Timestamp

4/17/2014, 11:57:16 AM

Confirmations

6,316,639

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f27ddd007592c7b145d24f5ef739fd4ad39bf400a877f23bde0d28de37ace6e2

Transactions (5)

Coinbasee4d0ae5783742e…41c7e0d5af68b4

1 in → 1 out8.6600 XPM116 B

AbwWkWZt…kawDhufa

551900dce80bef…b413552fc4a7f7

4 in → 1 out35.0000 XPM499 B

AY6xDs3M…yv92NwRM

86d0d024b5737f…673c9d7fbdb0a0

1 in → 2 out8.6900 XPM227 B

ARkcXaVK…SX11tmUe AGzuhBha…xzp4nRg2

ee40cb593a17fb…48e22b2f5c3668

1 in → 2 out8.6900 XPM227 B

ARv4Qgdi…NXqhEmwt AdobpKjj…M9auVuzw

5e275bd0fc8c6d…13b1f11db2b1ea

1 in → 2 out8.6900 XPM226 B

AZgATnHZ…KtRNfLYF AN5egmZF…vjXqiPGT

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.

1.798 × 10⁹⁸(99-digit number)

17981004981537692256…75698668526576517119

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

1.798 × 10⁹⁸(99-digit number)

17981004981537692256…75698668526576517119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.798 × 10⁹⁸(99-digit number)

17981004981537692256…75698668526576517121

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

3.596 × 10⁹⁸(99-digit number)

35962009963075384513…51397337053153034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.596 × 10⁹⁸(99-digit number)

35962009963075384513…51397337053153034241

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

7.192 × 10⁹⁸(99-digit number)

71924019926150769027…02794674106306068479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.192 × 10⁹⁸(99-digit number)

71924019926150769027…02794674106306068481

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

1.438 × 10⁹⁹(100-digit number)

14384803985230153805…05589348212612136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.438 × 10⁹⁹(100-digit number)

14384803985230153805…05589348212612136961

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

2.876 × 10⁹⁹(100-digit number)

28769607970460307611…11178696425224273919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.876 × 10⁹⁹(100-digit number)

28769607970460307611…11178696425224273921

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 #497,227

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