Block #337,176

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 11:53:33 AM · Difficulty 10.1388 · 6,480,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f7bf34706d3dfb7627392232a1f36aec8c1bbc94b34c49430d88d19d12be211

View on Chainz ↗

Height

#337,176

Difficulty

10.138850

Transactions

Size

950 B

Version

Bits

0a238baa

Nonce

235,370

Timestamp

12/31/2013, 11:53:33 AM

Confirmations

6,480,792

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ba052c7001a8b15d7aea9223ed460a45bab0a2b8d2f23752c651cb3a450b2798

Transactions (3)

Coinbase108aa871426359…53728dd888a00b

1 in → 1 out9.7300 XPM110 B

AeKNrjNj…1NEq95Ta

e9e72610ed4dd3…67aa9453f2de1f

3 in → 2 out31.8800 XPM523 B

AJtcYzHf…A1nq73qL AKn8yab8…VR8hJjuZ

a1cbf565176190…aae7fe9bb0a52e

1 in → 2 out2.5437 XPM226 B

APrrzejV…kGuwn3qT AMNPUhwn…fDHYSk5S

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.

1.046 × 10⁹⁶(97-digit number)

10461650826581966863…42500177452529122069

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

1.046 × 10⁹⁶(97-digit number)

10461650826581966863…42500177452529122069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.046 × 10⁹⁶(97-digit number)

10461650826581966863…42500177452529122071

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

2.092 × 10⁹⁶(97-digit number)

20923301653163933726…85000354905058244139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.092 × 10⁹⁶(97-digit number)

20923301653163933726…85000354905058244141

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

4.184 × 10⁹⁶(97-digit number)

41846603306327867453…70000709810116488279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.184 × 10⁹⁶(97-digit number)

41846603306327867453…70000709810116488281

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

8.369 × 10⁹⁶(97-digit number)

83693206612655734907…40001419620232976559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.369 × 10⁹⁶(97-digit number)

83693206612655734907…40001419620232976561

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

1.673 × 10⁹⁷(98-digit number)

16738641322531146981…80002839240465953119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.673 × 10⁹⁷(98-digit number)

16738641322531146981…80002839240465953121

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

Block #337,176

Cookie Preferences