Block #164,806

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/14/2013, 9:38:20 PM · Difficulty 9.8639 · 6,662,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d916d0511476a6149272a3ee5d2e880133877d96c6e5dbd1dbd4663e9c0dd53f

View on Chainz ↗

Height

#164,806

Difficulty

9.863853

Transactions

Size

572 B

Version

Bits

09dd257f

Nonce

42,808

Timestamp

9/14/2013, 9:38:20 PM

Confirmations

6,662,093

Mined by

⛏️ P2SHAM1A9CZLPnH51axL7hPRTWjkm6as4Lpogj

Merkle Root

c69c95d2c79f7476d60161b3920a0f5fb6a7f0d9e35f660e35bf16efa8579cb9

Transactions (2)

Coinbasec4854e5bb286e1…fe220379c47a7c

1 in → 1 out10.2700 XPM109 B

AM1A9CZL…as4Lpogj

024defd5708270…9c9c3c4677c667

2 in → 2 out25.0100 XPM374 B

ARKqKmwM…93wZogJX AbhWjNtr…ZGT63E3Y

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.

2.057 × 10⁹²(93-digit number)

20578278802250052946…97590164898263569919

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

2.057 × 10⁹²(93-digit number)

20578278802250052946…97590164898263569919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.057 × 10⁹²(93-digit number)

20578278802250052946…97590164898263569921

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

4.115 × 10⁹²(93-digit number)

41156557604500105893…95180329796527139839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.115 × 10⁹²(93-digit number)

41156557604500105893…95180329796527139841

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

8.231 × 10⁹²(93-digit number)

82313115209000211786…90360659593054279679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.231 × 10⁹²(93-digit number)

82313115209000211786…90360659593054279681

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

1.646 × 10⁹³(94-digit number)

16462623041800042357…80721319186108559359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.646 × 10⁹³(94-digit number)

16462623041800042357…80721319186108559361

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

3.292 × 10⁹³(94-digit number)

32925246083600084714…61442638372217118719

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 #164,806

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