Block #179,551

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/25/2013, 4:16:37 AM · Difficulty 9.8633 · 6,630,303 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12af0611f3117e6e629b32bc7e202b23050698bc5aa56958ae2b24de0e1c1f6f

View on Chainz ↗

Height

#179,551

Difficulty

9.863293

Transactions

Size

595 B

Version

Bits

09dd00c4

Nonce

1,164,807,924

Timestamp

9/25/2013, 4:16:37 AM

Confirmations

6,630,303

Mined by

⛏️ _RBc{AJCCNvEZ7QwzTUEfYPwXoS9dvEgX1b1gmx

Merkle Root

f917e939c8f02cff99b0939d72081d0527dadf8bb4de50f9ab5e38dbc0d43eb1

Transactions (1)

Coinbasef917e939c8f02c…5e38dbc0d43eb1

1 in → 13 out10.2600 XPM504 B

AJCCNvEZ…gX1b1gmx ANyjx1Xw…3yYqVfUy AV4rziFj…QhTLsLyZ ANscdPEm…b8DYdwDD AeckU1Kq…a9chH61d

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.

9.291 × 10⁹⁷(98-digit number)

92912208188464653327…07859511468697499839

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

9.291 × 10⁹⁷(98-digit number)

92912208188464653327…07859511468697499839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.291 × 10⁹⁷(98-digit number)

92912208188464653327…07859511468697499841

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

1.858 × 10⁹⁸(99-digit number)

18582441637692930665…15719022937394999679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.858 × 10⁹⁸(99-digit number)

18582441637692930665…15719022937394999681

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

3.716 × 10⁹⁸(99-digit number)

37164883275385861331…31438045874789999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.716 × 10⁹⁸(99-digit number)

37164883275385861331…31438045874789999361

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

7.432 × 10⁹⁸(99-digit number)

74329766550771722662…62876091749579998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.432 × 10⁹⁸(99-digit number)

74329766550771722662…62876091749579998721

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

1.486 × 10⁹⁹(100-digit number)

14865953310154344532…25752183499159997439

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 #179,551

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