Block #515,300

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/28/2014, 5:17:37 PM · Difficulty 10.8405 · 6,293,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

edf10ca9501889b2789e321bbf75aa05445eb27d37d1a7b73f4d7d2d6baf7bdd

View on Chainz ↗

Height

#515,300

Difficulty

10.840458

Transactions

Size

798 B

Version

Bits

0ad72844

Nonce

18,106

Timestamp

4/28/2014, 5:17:37 PM

Confirmations

6,293,417

Mined by

⛏️ aS^2!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b68f4bfc5d879e9efbc6d753d08f595eac80ee71e7509d2b73263626ab577442

Transactions (1)

Coinbaseb68f4bfc5d879e…263626ab577442

1 in → 19 out8.5000 XPM709 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf

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.

1.016 × 10⁹³(94-digit number)

10169208763493728071…15284974950439254399

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

1.016 × 10⁹³(94-digit number)

10169208763493728071…15284974950439254399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.016 × 10⁹³(94-digit number)

10169208763493728071…15284974950439254401

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

2.033 × 10⁹³(94-digit number)

20338417526987456143…30569949900878508799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.033 × 10⁹³(94-digit number)

20338417526987456143…30569949900878508801

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

4.067 × 10⁹³(94-digit number)

40676835053974912287…61139899801757017599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.067 × 10⁹³(94-digit number)

40676835053974912287…61139899801757017601

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

8.135 × 10⁹³(94-digit number)

81353670107949824575…22279799603514035199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.135 × 10⁹³(94-digit number)

81353670107949824575…22279799603514035201

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

1.627 × 10⁹⁴(95-digit number)

16270734021589964915…44559599207028070399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.627 × 10⁹⁴(95-digit number)

16270734021589964915…44559599207028070401

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 #515,300

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