Block #337,181

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 11:58:50 AM · Difficulty 10.1387 · 6,468,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa8f1b3b62ea3e0867bbe26bfddc87c978b5d11ccd61ba1a4cae7e4bfa93ff33

View on Chainz ↗

Height

#337,181

Difficulty

10.138654

Transactions

Size

1.37 KB

Version

Bits

0a237ecd

Nonce

142,962

Timestamp

12/31/2013, 11:58:50 AM

Confirmations

6,468,511

Mined by

⛏️ P2SHAdY9yW6TbgqJyEUBVgcqBXskZaELmWTSU4

Merkle Root

d1a5d871da61a152b03a3fb404689763dd99a9fb31676b876d8348a1bdea5bbf

Transactions (5)

Coinbaseeef4b321a04a07…4ccbdb9c0b5c2a

1 in → 1 out9.7500 XPM109 B

AdY9yW6T…ELmWTSU4

21b4ec186109aa…cce4e5ea458659

2 in → 2 out10.2098 XPM374 B

AG2gjCtb…t5V3PgFG Aa2JA2Lk…R4Q3S5WK

f5c62f8e251b08…7795228730840e

2 in → 2 out10.2028 XPM374 B

AT2dDesH…gZpUzTkH AY4uM53e…yee8uDKH

31456607d3b9f3…ac04121ab7ad4a

1 in → 2 out6.2391 XPM227 B

Aauv3owM…q5ehyfKe Abkp6z5P…hQ5DLwan

465f39bf2ab378…174f5d72995a2b

1 in → 2 out1.5821 XPM226 B

AMBaesuK…6AGZoQG4 ASSGXdv6…wb541wPL

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.

4.566 × 10⁹⁹(100-digit number)

45661856045439433145…51850704364623638689

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

4.566 × 10⁹⁹(100-digit number)

45661856045439433145…51850704364623638689

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.566 × 10⁹⁹(100-digit number)

45661856045439433145…51850704364623638691

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

9.132 × 10⁹⁹(100-digit number)

91323712090878866290…03701408729247277379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.132 × 10⁹⁹(100-digit number)

91323712090878866290…03701408729247277381

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

1.826 × 10¹⁰⁰(101-digit number)

18264742418175773258…07402817458494554759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.826 × 10¹⁰⁰(101-digit number)

18264742418175773258…07402817458494554761

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

3.652 × 10¹⁰⁰(101-digit number)

36529484836351546516…14805634916989109519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.652 × 10¹⁰⁰(101-digit number)

36529484836351546516…14805634916989109521

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

7.305 × 10¹⁰⁰(101-digit number)

73058969672703093032…29611269833978219039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.305 × 10¹⁰⁰(101-digit number)

73058969672703093032…29611269833978219041

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