Block #1,267,504

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/5/2015, 2:07:00 AM · Difficulty 10.8192 · 5,558,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0af804898554e442e4e30dd2bc082b0969d21bf1a7d6faf5e514ab17a837c1c0

View on Chainz ↗

Height

#1,267,504

Difficulty

10.819171

Transactions

Size

628 B

Version

Bits

0ad1b539

Nonce

42,815,853

Timestamp

10/5/2015, 2:07:00 AM

Confirmations

5,558,932

Mined by

⛏️ P2SHAZqnCo3VmBGouz2Q6KStCRrbZogSr2A3Mr

Merkle Root

047025da13e1b61166805d48d0c7ba2d20b265945bf694c312aaeaf36d632799

Transactions (2)

Coinbasea1669952c89cfe…f2f576d032310f

1 in → 1 out8.5400 XPM109 B

AZqnCo3V…gSr2A3Mr

0c23f9f28037ae…94f8a3ed80de9b

1 in → 8 out70.3158 XPM430 B

AVjz5L9w…xuFRGF8g ATPJ4yMa…oUsunS3P AbUgRDkj…RPTqufBa AFqAiWtG…JNZAjpHt ARQevyy8…dy5X6yrG

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.

7.302 × 10⁹¹(92-digit number)

73029331429799620885…93964911187655221299

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

7.302 × 10⁹¹(92-digit number)

73029331429799620885…93964911187655221299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.302 × 10⁹¹(92-digit number)

73029331429799620885…93964911187655221301

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

1.460 × 10⁹²(93-digit number)

14605866285959924177…87929822375310442599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.460 × 10⁹²(93-digit number)

14605866285959924177…87929822375310442601

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

2.921 × 10⁹²(93-digit number)

29211732571919848354…75859644750620885199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.921 × 10⁹²(93-digit number)

29211732571919848354…75859644750620885201

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

5.842 × 10⁹²(93-digit number)

58423465143839696708…51719289501241770399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.842 × 10⁹²(93-digit number)

58423465143839696708…51719289501241770401

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

1.168 × 10⁹³(94-digit number)

11684693028767939341…03438579002483540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.168 × 10⁹³(94-digit number)

11684693028767939341…03438579002483540801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,267,504

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