Block #164,849

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/14/2013, 10:15:37 PM · Difficulty 9.8640 · 6,639,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3578bf555519d5547b94fd998d08cf65ddc37a820cfac6e28a5ad46c5c0cce30

View on Chainz ↗

Height

#164,849

Difficulty

9.864036

Transactions

Size

4.80 KB

Version

Bits

09dd3176

Nonce

160,186

Timestamp

9/14/2013, 10:15:37 PM

Confirmations

6,639,366

Mined by

⛏️ P2SHAU6rDkaxgiFN8dZ9R9xPqkD694w1ymuvfQ

Merkle Root

10724cd7a7f0681cbb6096cffd9d74a6cc2a3f391be1ce0f8aa87d37005ca7ab

Transactions (3)

Coinbase41920593a7f3e7…1f505c482c5a5f

1 in → 1 out10.3200 XPM109 B

AU6rDkax…w1ymuvfQ

8f54b821665933…116e42a9b4a88b

39 in → 2 out400.6300 XPM4.42 KB

AbxSykSg…BX71twYi AMCWARXQ…VyQK5P4T

751dece549bb54…ed39006102eb42

1 in → 2 out10.2600 XPM193 B

AFz9fXym…wh4UqpkL AZnTRzUK…gEDUmGoo

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.

8.719 × 10⁹³(94-digit number)

87196958677452114392…92251159129591752959

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

8.719 × 10⁹³(94-digit number)

87196958677452114392…92251159129591752959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.719 × 10⁹³(94-digit number)

87196958677452114392…92251159129591752961

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

1.743 × 10⁹⁴(95-digit number)

17439391735490422878…84502318259183505919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.743 × 10⁹⁴(95-digit number)

17439391735490422878…84502318259183505921

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

3.487 × 10⁹⁴(95-digit number)

34878783470980845757…69004636518367011839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.487 × 10⁹⁴(95-digit number)

34878783470980845757…69004636518367011841

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

6.975 × 10⁹⁴(95-digit number)

69757566941961691514…38009273036734023679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.975 × 10⁹⁴(95-digit number)

69757566941961691514…38009273036734023681

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

1.395 × 10⁹⁵(96-digit number)

13951513388392338302…76018546073468047359

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