Block #337,628

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 7:53:19 PM · Difficulty 10.1339 · 6,458,181 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1277f9ab254926089cced8484b10f4b60083b8f5af2e8e82997185108bc35bd1

View on Chainz ↗

Height

#337,628

Difficulty

10.133861

Transactions

Size

1.64 KB

Version

Bits

0a2244b8

Nonce

34,811

Timestamp

12/31/2013, 7:53:19 PM

Confirmations

6,458,181

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

3a9c0e2a973b1aa177088e457cfe1bbd7c2e45b9737a98632eaede7534e21191

Transactions (5)

Coinbase7f8aecf7ef07b3…850be8ac56dba3

1 in → 1 out9.7600 XPM110 B

AeKNrjNj…1NEq95Ta

1600bf390b66e6…ae916b5653c7ad

4 in → 1 out937.9000 XPM637 B

AeJpFYeB…ysJkjV2a

74548d92d135cb…b764c04c6d723b

1 in → 1 out9.6800 XPM158 B

AFqYA8s7…xpFKHo7K

c59d6a20da605d…68201f78e51b92

1 in → 1 out9.7300 XPM158 B

AFqYA8s7…xpFKHo7K

73c9d246150625…911d6813098764

3 in → 2 out1.0563 XPM522 B

AREf5D61…t5A4aZez Adw1mrbk…t4Ve1nMt

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.

6.530 × 10⁹⁷(98-digit number)

65304374017290638977…81572347161611865599

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

6.530 × 10⁹⁷(98-digit number)

65304374017290638977…81572347161611865599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.530 × 10⁹⁷(98-digit number)

65304374017290638977…81572347161611865601

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

1.306 × 10⁹⁸(99-digit number)

13060874803458127795…63144694323223731199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.306 × 10⁹⁸(99-digit number)

13060874803458127795…63144694323223731201

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

2.612 × 10⁹⁸(99-digit number)

26121749606916255591…26289388646447462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.612 × 10⁹⁸(99-digit number)

26121749606916255591…26289388646447462401

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

5.224 × 10⁹⁸(99-digit number)

52243499213832511182…52578777292894924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.224 × 10⁹⁸(99-digit number)

52243499213832511182…52578777292894924801

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

1.044 × 10⁹⁹(100-digit number)

10448699842766502236…05157554585789849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.044 × 10⁹⁹(100-digit number)

10448699842766502236…05157554585789849601

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