Block #496,037

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 9:41:52 PM · Difficulty 10.7483 · 6,306,984 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36f300add2cc6ba4860d1570b21bce236cfe1cfe425fe5929d051428969f80c1

View on Chainz ↗

Height

#496,037

Difficulty

10.748311

Transactions

Size

766 B

Version

Bits

0abf9155

Nonce

11,055

Timestamp

4/16/2014, 9:41:52 PM

Confirmations

6,306,984

Mined by

⛏️ aSNAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3feabedcd3cb1ac3d0ff3763f76c0d075fdcfba1cf24ac44dc46c00a508f24d2

Transactions (1)

Coinbase3feabedcd3cb1a…46c00a508f24d2

1 in → 18 out8.6400 XPM675 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

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.

3.110 × 10⁹⁶(97-digit number)

31104287178065655043…59982957022938015999

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

3.110 × 10⁹⁶(97-digit number)

31104287178065655043…59982957022938015999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.110 × 10⁹⁶(97-digit number)

31104287178065655043…59982957022938016001

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

6.220 × 10⁹⁶(97-digit number)

62208574356131310087…19965914045876031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.220 × 10⁹⁶(97-digit number)

62208574356131310087…19965914045876032001

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

1.244 × 10⁹⁷(98-digit number)

12441714871226262017…39931828091752063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.244 × 10⁹⁷(98-digit number)

12441714871226262017…39931828091752064001

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

2.488 × 10⁹⁷(98-digit number)

24883429742452524034…79863656183504127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.488 × 10⁹⁷(98-digit number)

24883429742452524034…79863656183504128001

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

4.976 × 10⁹⁷(98-digit number)

49766859484905048069…59727312367008255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.976 × 10⁹⁷(98-digit number)

49766859484905048069…59727312367008256001

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