Block #496,391

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 1:57:00 AM · Difficulty 10.7532 · 6,295,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab59708e3c12604e578426e6d364088ae3554dcb740e6f27de429ba1d727fb28

View on Chainz ↗

Height

#496,391

Difficulty

10.753220

Transactions

Size

886 B

Version

Bits

0ac0d301

Nonce

468,712,589

Timestamp

4/17/2014, 1:57:00 AM

Confirmations

6,295,839

Merkle Root

e0f3e8ff16480221d06c2636f2eb6321e1eb12a6175868a287082b637f5c79fe

Transactions (4)

Coinbasef85bf594310cd9…22b92db9d05715

1 in → 1 out8.6600 XPM116 B

AbwWkWZt…kawDhufa

f2f6d0d7e8406f…3b1427c4b2d1dc

1 in → 2 out8.7200 XPM226 B

AGhc2RAk…AnpTBccY AUeWQBH9…rmgJWJFp

b6dd19e2dde9e4…892a380a5dafd0

1 in → 2 out7.1738 XPM226 B

AdYE6p6N…gTYqQsr4 AawSwHyt…BmeWAmZG

7e1111a54afc19…8c5e7d0aacbdc4

1 in → 2 out5.0500 XPM227 B

AWAnj1wA…kTV1MBmQ AMU8nEj9…Eo32pqxr

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.

4.059 × 10⁹⁷(98-digit number)

40590233712659077170…77085646517257563999

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

4.059 × 10⁹⁷(98-digit number)

40590233712659077170…77085646517257563999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.059 × 10⁹⁷(98-digit number)

40590233712659077170…77085646517257564001

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

8.118 × 10⁹⁷(98-digit number)

81180467425318154340…54171293034515127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.118 × 10⁹⁷(98-digit number)

81180467425318154340…54171293034515128001

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

1.623 × 10⁹⁸(99-digit number)

16236093485063630868…08342586069030255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.623 × 10⁹⁸(99-digit number)

16236093485063630868…08342586069030256001

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

3.247 × 10⁹⁸(99-digit number)

32472186970127261736…16685172138060511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.247 × 10⁹⁸(99-digit number)

32472186970127261736…16685172138060512001

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

6.494 × 10⁹⁸(99-digit number)

64944373940254523472…33370344276121023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.494 × 10⁹⁸(99-digit number)

64944373940254523472…33370344276121024001

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