Block #337,664

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 8:39:03 PM · Difficulty 10.1327 · 6,458,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9591eae80b970d7e5700bed601378d1e17c74cf81934be3622f73ebdcab8ebea

View on Chainz ↗

Height

#337,664

Difficulty

10.132694

Transactions

Size

893 B

Version

Bits

0a21f83b

Nonce

352,401

Timestamp

12/31/2013, 8:39:03 PM

Confirmations

6,458,071

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e6fd76888d81941ca30ae1b40f53f6ea9fefe5d725474e0552b8745368c9e71c

Transactions (2)

Coinbasee92e5eacf6b77d…7a21ba154839ed

1 in → 1 out9.7400 XPM110 B

AeKNrjNj…1NEq95Ta

ad083664fdb7db…efad45f39a47bc

3 in → 10 out29.2900 XPM690 B

AKUmd8UD…5RbqPUAS AdmVExw4…1253dK5x AU9LxgoZ…JFUQUYbN AeKNrjNj…1NEq95Ta AeHnQ89o…5XTei6jt

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.

1.003 × 10¹⁰²(103-digit number)

10032346956827335233…18288797743341939599

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

1.003 × 10¹⁰²(103-digit number)

10032346956827335233…18288797743341939599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10¹⁰²(103-digit number)

10032346956827335233…18288797743341939601

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

2.006 × 10¹⁰²(103-digit number)

20064693913654670467…36577595486683879199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.006 × 10¹⁰²(103-digit number)

20064693913654670467…36577595486683879201

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

4.012 × 10¹⁰²(103-digit number)

40129387827309340934…73155190973367758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.012 × 10¹⁰²(103-digit number)

40129387827309340934…73155190973367758401

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

8.025 × 10¹⁰²(103-digit number)

80258775654618681868…46310381946735516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.025 × 10¹⁰²(103-digit number)

80258775654618681868…46310381946735516801

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

1.605 × 10¹⁰³(104-digit number)

16051755130923736373…92620763893471033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.605 × 10¹⁰³(104-digit number)

16051755130923736373…92620763893471033601

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