Block #193,156

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 8:31:24 AM · Difficulty 9.8753 · 6,611,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5dfddc8f53bc4a16d07c6964b9596cd83a5039e130a0468ea3b4b2ea4b113dc7

View on Chainz ↗

Height

#193,156

Difficulty

9.875331

Transactions

Size

1.10 KB

Version

Bits

09e015ac

Nonce

5,018

Timestamp

10/4/2013, 8:31:24 AM

Confirmations

6,611,779

Mined by

⛏️ P2SHAPgo3PHAZwGSB8pKnZ3dFRHAFCFuMZQfxN

Merkle Root

3cdc60ca817a6feca7c5c220fc82f0fa3d98117d84e105bd566603cd1706e690

Transactions (4)

Coinbasebf448689f9a7ea…4d2edc9408a43d

1 in → 1 out10.2700 XPM109 B

APgo3PHA…FuMZQfxN

27169dd0d98b6c…e7faff57021ac1

2 in → 7 out20.4900 XPM478 B

AQXUSoBL…CzbjKp8b AFq51nP4…FqYfXapg AKyT5sag…P1gmPYoR Ac5sZcdP…kzV4eckG AFvfCa1W…3pZgbFWa

2243a9ed75fe05…8294b250650784

1 in → 2 out10.2300 XPM227 B

ARKbHEz9…KTxn9TKo AdWp2YRv…FDtt217a

0a6536dc31129b…9dd8e71701781f

1 in → 2 out8.2004 XPM226 B

AbbMmrFP…3rg6n5iA ATuWxsBa…dKFZ3gRq

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.

2.010 × 10⁹⁶(97-digit number)

20103419880345392338…83107320210599599679

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

2.010 × 10⁹⁶(97-digit number)

20103419880345392338…83107320210599599679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.010 × 10⁹⁶(97-digit number)

20103419880345392338…83107320210599599681

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

4.020 × 10⁹⁶(97-digit number)

40206839760690784677…66214640421199199359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.020 × 10⁹⁶(97-digit number)

40206839760690784677…66214640421199199361

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

8.041 × 10⁹⁶(97-digit number)

80413679521381569354…32429280842398398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.041 × 10⁹⁶(97-digit number)

80413679521381569354…32429280842398398721

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

1.608 × 10⁹⁷(98-digit number)

16082735904276313870…64858561684796797439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.608 × 10⁹⁷(98-digit number)

16082735904276313870…64858561684796797441

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

3.216 × 10⁹⁷(98-digit number)

32165471808552627741…29717123369593594879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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