Block #134,370

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 12:31:48 AM · Difficulty 9.8034 · 6,661,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8207fb64917c7bb5e28d163cd154e94e4d3c1a42866f69205cb7367cd597006d

View on Chainz ↗

Height

#134,370

Difficulty

9.803448

Transactions

Size

1.01 KB

Version

Bits

09cdaec2

Nonce

98,332

Timestamp

8/26/2013, 12:31:48 AM

Confirmations

6,661,206

Mined by

⛏️ P2SHAXiuhqLMgrEy6TQQhtFEjy5mHUBnWxzTFY

Merkle Root

3c36efc7cdd8913c6bc48fdbc08386ac4f4ddbb5b461aeba89e248e5ebd44b0d

Transactions (4)

Coinbase30c05713c014df…2208624dd4fcb3

1 in → 1 out10.4200 XPM109 B

AXiuhqLM…BnWxzTFY

e1aaa61bfc702a…c1164097689053

1 in → 1 out10.4200 XPM158 B

AH9D5N1B…4NXoLsWQ

0326c398981e9f…dcc8e25b4cf18b

1 in → 1 out10.4800 XPM157 B

AH9D5N1B…4NXoLsWQ

3600bafd5d52bf…0ba356555a4939

3 in → 2 out5.3130 XPM524 B

APjCChRp…u1a7otyd AHnV9s5Z…jWs1Jf44

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.

2.522 × 10⁹²(93-digit number)

25220411511061264013…94743125265778756639

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

2.522 × 10⁹²(93-digit number)

25220411511061264013…94743125265778756639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.522 × 10⁹²(93-digit number)

25220411511061264013…94743125265778756641

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

5.044 × 10⁹²(93-digit number)

50440823022122528027…89486250531557513279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.044 × 10⁹²(93-digit number)

50440823022122528027…89486250531557513281

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

1.008 × 10⁹³(94-digit number)

10088164604424505605…78972501063115026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.008 × 10⁹³(94-digit number)

10088164604424505605…78972501063115026561

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

2.017 × 10⁹³(94-digit number)

20176329208849011210…57945002126230053119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.017 × 10⁹³(94-digit number)

20176329208849011210…57945002126230053121

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

4.035 × 10⁹³(94-digit number)

40352658417698022421…15890004252460106239

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