Block #502,113

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/20/2014, 5:26:37 AM · Difficulty 10.8062 · 6,299,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c7773eab2b073c15aefff23e076c0777257d3a10a98450f8412198aa132aab1

View on Chainz ↗

Height

#502,113

Difficulty

10.806200

Transactions

Size

663 B

Version

Bits

0ace631e

Nonce

56,260

Timestamp

4/20/2014, 5:26:37 AM

Confirmations

6,299,700

Mined by

⛏️ aaSSXAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b39f30f87c3bb7d9d95f567f4a3c6441ecdc52eba17b5f1fab1628c29ffee9a6

Transactions (1)

Coinbaseb39f30f87c3bb7…1628c29ffee9a6

1 in → 15 out8.5500 XPM573 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j 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.

3.798 × 10⁹⁴(95-digit number)

37983958750020608315…62884405846232350719

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

3.798 × 10⁹⁴(95-digit number)

37983958750020608315…62884405846232350719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.798 × 10⁹⁴(95-digit number)

37983958750020608315…62884405846232350721

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

7.596 × 10⁹⁴(95-digit number)

75967917500041216630…25768811692464701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.596 × 10⁹⁴(95-digit number)

75967917500041216630…25768811692464701441

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

1.519 × 10⁹⁵(96-digit number)

15193583500008243326…51537623384929402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.519 × 10⁹⁵(96-digit number)

15193583500008243326…51537623384929402881

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

3.038 × 10⁹⁵(96-digit number)

30387167000016486652…03075246769858805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.038 × 10⁹⁵(96-digit number)

30387167000016486652…03075246769858805761

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

6.077 × 10⁹⁵(96-digit number)

60774334000032973304…06150493539717611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.077 × 10⁹⁵(96-digit number)

60774334000032973304…06150493539717611521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.215 × 10⁹⁶(97-digit number)

12154866800006594660…12300987079435223039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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