Block #328,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 3:49:46 PM · Difficulty 10.1697 · 6,474,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1049d8a977d7144ea65438eff84db3f8deafac76903bdcd82527f227d2dced22

View on Chainz ↗

Height

#328,976

Difficulty

10.169715

Transactions

Size

1.37 KB

Version

Bits

0a2b7279

Nonce

158,957

Timestamp

12/25/2013, 3:49:46 PM

Confirmations

6,474,302

Mined by

⛏️ P2SHAbueRAwxb11A1N6ojNF3A6miCPzfpi68tC

Merkle Root

7cb42b631515f9839ec916ce39a97dd8739c15f7b0407e112fd63ab58cd8c3c3

Transactions (5)

Coinbase8acada3ffa475f…b1fe1056adb50e

1 in → 1 out9.6900 XPM109 B

AbueRAwx…zfpi68tC

e2ec6b335caeb0…7fc6619208d29c

1 in → 2 out4.4638 XPM225 B

AMHhQCPk…3YvojiHh AGusNSbi…TMhj3ShN

61554a3593cb87…b3c83e9c819f05

1 in → 2 out3.4514 XPM226 B

Abodb6cY…7sq489d2 AYjaRmHw…1YGz3NQm

290d3b30a4a530…21164758d74d69

1 in → 2 out4.4117 XPM227 B

AbJDWL7j…2X5Yb4qH ALTLJarX…SY7ea82E

5fe3db49847bf6…ff772ec96fa1c8

3 in → 2 out1.1789 XPM521 B

AYAVkZuY…Jz9dDUHZ ARtYftjF…RZKJQ3ey

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.

1.168 × 10¹⁰¹(102-digit number)

11687718714171582677…01852751580579901439

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

1.168 × 10¹⁰¹(102-digit number)

11687718714171582677…01852751580579901439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.168 × 10¹⁰¹(102-digit number)

11687718714171582677…01852751580579901441

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

2.337 × 10¹⁰¹(102-digit number)

23375437428343165355…03705503161159802879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.337 × 10¹⁰¹(102-digit number)

23375437428343165355…03705503161159802881

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

4.675 × 10¹⁰¹(102-digit number)

46750874856686330711…07411006322319605759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.675 × 10¹⁰¹(102-digit number)

46750874856686330711…07411006322319605761

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

9.350 × 10¹⁰¹(102-digit number)

93501749713372661422…14822012644639211519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.350 × 10¹⁰¹(102-digit number)

93501749713372661422…14822012644639211521

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

1.870 × 10¹⁰²(103-digit number)

18700349942674532284…29644025289278423039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.870 × 10¹⁰²(103-digit number)

18700349942674532284…29644025289278423041

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