Block #202,107

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 12:35:40 AM · Difficulty 9.8944 · 6,593,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1735c70aa5dc120396be9938cc448419d858fb541d22b902622db8d0a844675

View on Chainz ↗

Height

#202,107

Difficulty

9.894423

Transactions

Size

1.22 KB

Version

Bits

09e4f8ed

Nonce

148,823

Timestamp

10/10/2013, 12:35:40 AM

Confirmations

6,593,874

Mined by

⛏️ P2SHASMAUr2czqkyA6uP723ez5mTkqY7SPtauE

Merkle Root

86546dca98e00ad968d5568e929fb35b092fcd35802205c0177ac4e993a616fc

Transactions (3)

Coinbaseda04ccc5114334…632a362f25ace6

1 in → 1 out10.2200 XPM109 B

ASMAUr2c…Y7SPtauE

eede0ea2b29010…02214efe4640c1

5 in → 2 out51.1000 XPM819 B

AHUgkEqf…b9YEDMVk AUz8thG8…aBq85Fqh

0d9b25a972daaa…f0af37dfdce29c

1 in → 2 out2.4617 XPM226 B

AH7nXzgB…K4VVPw3D AXCCsfyG…SSSFr1ZK

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.

5.266 × 10⁹⁶(97-digit number)

52666054882048995120…83751835189856027339

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

5.266 × 10⁹⁶(97-digit number)

52666054882048995120…83751835189856027339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.266 × 10⁹⁶(97-digit number)

52666054882048995120…83751835189856027341

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

1.053 × 10⁹⁷(98-digit number)

10533210976409799024…67503670379712054679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.053 × 10⁹⁷(98-digit number)

10533210976409799024…67503670379712054681

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

2.106 × 10⁹⁷(98-digit number)

21066421952819598048…35007340759424109359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.106 × 10⁹⁷(98-digit number)

21066421952819598048…35007340759424109361

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

4.213 × 10⁹⁷(98-digit number)

42132843905639196096…70014681518848218719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.213 × 10⁹⁷(98-digit number)

42132843905639196096…70014681518848218721

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

8.426 × 10⁹⁷(98-digit number)

84265687811278392192…40029363037696437439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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