Block #162,259

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 5:03:46 AM · Difficulty 9.8610 · 6,652,885 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2b57ac374e47493905c897dcf148b100005582428156941708ef6f42e043de8

View on Chainz ↗

Height

#162,259

Difficulty

9.861002

Transactions

Size

2.95 KB

Version

Bits

09dc6aa6

Nonce

88,502

Timestamp

9/13/2013, 5:03:46 AM

Confirmations

6,652,885

Mined by

⛏️ P2SHASYqk3tgsSSAdBeYAUZbsvx5UzoGUnTrkb

Merkle Root

7287528a3accdd30c5824092c33833df0ef2aeb17054fb7c016a6ba98c029f78

Transactions (4)

Coinbaseeec2dcc4d26713…81b0abe3929db7

1 in → 1 out10.3200 XPM109 B

ASYqk3tg…oGUnTrkb

1652ca863d1a6c…c8c5fee17549ec

1 in → 1 out10.2600 XPM157 B

AQt7xHtg…AXmNFrUW

eb0ffca245a914…26629a8919fae4

21 in → 1 out215.3300 XPM2.38 KB

AaZTHvEh…QXHS2iBB

6e57730dc9ea5e…f485d882f6065c

1 in → 2 out0.3300 XPM227 B

AV1V5bMx…YqKJg4EE AHSjPeL7…o1c6DURU

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.

3.507 × 10⁹³(94-digit number)

35073478269992047440…48140062324871579419

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

3.507 × 10⁹³(94-digit number)

35073478269992047440…48140062324871579419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.507 × 10⁹³(94-digit number)

35073478269992047440…48140062324871579421

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

7.014 × 10⁹³(94-digit number)

70146956539984094881…96280124649743158839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.014 × 10⁹³(94-digit number)

70146956539984094881…96280124649743158841

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

1.402 × 10⁹⁴(95-digit number)

14029391307996818976…92560249299486317679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.402 × 10⁹⁴(95-digit number)

14029391307996818976…92560249299486317681

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

2.805 × 10⁹⁴(95-digit number)

28058782615993637952…85120498598972635359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.805 × 10⁹⁴(95-digit number)

28058782615993637952…85120498598972635361

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

5.611 × 10⁹⁴(95-digit number)

56117565231987275905…70240997197945270719

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 #162,259

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