Block #141,629

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 10:48:07 AM · Difficulty 9.8353 · 6,662,567 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95f705e4e0bea45771e19d6cded5e22d3f2d6629d2d8b49445001ecba6acaa56

View on Chainz ↗

Height

#141,629

Difficulty

9.835275

Transactions

Size

882 B

Version

Bits

09d5d492

Nonce

28,571

Timestamp

8/30/2013, 10:48:07 AM

Confirmations

6,662,567

Mined by

⛏️ P2SHAQGz9h1x7euuJVUVqRVhcyEPS83RpsqhCW

Merkle Root

d22aa8f8d32a895d3f06083c36d953fcc39361eaf72ece91a9772a22d2f6927c

Transactions (4)

Coinbase02822fd9dd41d4…3610a8de9eb6da

1 in → 1 out10.3500 XPM109 B

AQGz9h1x…3RpsqhCW

8c4b504fcfc82b…713ae64b2f0366

1 in → 2 out1.3300 XPM226 B

Ae4ssmDA…vZSZMfbk AL8hqp9M…Tc3pKqTf

70fcf5c71355bc…d69bac251c663a

1 in → 2 out6.6338 XPM227 B

AMsr9Rez…6CvbYSL9 AS5W2rXx…Vt6dcetJ

2fb38fa27a0ab3…3efb49b9e95e5d

1 in → 2 out2.0939 XPM225 B

AepajDTG…SBqiu5Lf ATqDht7F…xHD53DYv

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.

8.005 × 10¹⁰⁶(107-digit number)

80053703149972837630…64345475255338815959

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

8.005 × 10¹⁰⁶(107-digit number)

80053703149972837630…64345475255338815959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.005 × 10¹⁰⁶(107-digit number)

80053703149972837630…64345475255338815961

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

1.601 × 10¹⁰⁷(108-digit number)

16010740629994567526…28690950510677631919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.601 × 10¹⁰⁷(108-digit number)

16010740629994567526…28690950510677631921

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

3.202 × 10¹⁰⁷(108-digit number)

32021481259989135052…57381901021355263839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.202 × 10¹⁰⁷(108-digit number)

32021481259989135052…57381901021355263841

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

6.404 × 10¹⁰⁷(108-digit number)

64042962519978270104…14763802042710527679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.404 × 10¹⁰⁷(108-digit number)

64042962519978270104…14763802042710527681

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

1.280 × 10¹⁰⁸(109-digit number)

12808592503995654020…29527604085421055359

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