Block #236,835

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 5:11:25 PM · Difficulty 9.9485 · 6,601,787 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09dd883353da5a6c3f9a5d3883c4d66a5eb3078dcaee74f69474ee78f7c8a294

View on Chainz ↗

Height

#236,835

Difficulty

9.948529

Transactions

Size

1.51 KB

Version

Bits

09f2d2cf

Nonce

432,138

Timestamp

10/31/2013, 5:11:25 PM

Confirmations

6,601,787

Mined by

⛏️ #RrAb1hhPziYwxnYhbN1NBo5h2U4CURi5woLf

Merkle Root

12b3ad42241deae9843281aafa402f4ded067556fd4f997e9a8df9c3dd2b03a3

Transactions (1)

Coinbase12b3ad42241dea…8df9c3dd2b03a3

1 in → 41 out10.0700 XPM1.42 KB

Ab1hhPzi…URi5woLf ANpPrsJp…YzdEphWb ANTtzNGc…NWu9L42o AQtzUSwq…htAuF3yC ANUaggy4…MWdrertQ

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.

1.274 × 10⁹¹(92-digit number)

12746236074333961990…18011164357150184319

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

1.274 × 10⁹¹(92-digit number)

12746236074333961990…18011164357150184319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.274 × 10⁹¹(92-digit number)

12746236074333961990…18011164357150184321

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

2.549 × 10⁹¹(92-digit number)

25492472148667923981…36022328714300368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.549 × 10⁹¹(92-digit number)

25492472148667923981…36022328714300368641

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

5.098 × 10⁹¹(92-digit number)

50984944297335847963…72044657428600737279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.098 × 10⁹¹(92-digit number)

50984944297335847963…72044657428600737281

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

1.019 × 10⁹²(93-digit number)

10196988859467169592…44089314857201474559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.019 × 10⁹²(93-digit number)

10196988859467169592…44089314857201474561

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

2.039 × 10⁹²(93-digit number)

20393977718934339185…88178629714402949119

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

Block #236,835

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