Block #1,246,313

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2015, 11:39:19 AM · Difficulty 10.7505 · 5,595,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0693c2bb6d25723da928ac1d1dc3fd1946fe089ddb05a2b8ca4bc3d75dbef545

View on Chainz ↗

Height

#1,246,313

Difficulty

10.750510

Transactions

Size

23.69 KB

Version

Bits

0ac02167

Nonce

1,196,165,588

Timestamp

9/21/2015, 11:39:19 AM

Confirmations

5,595,464

Mined by

⛏️ P2SHAaun7VkjiYS6X2W3JfYjHfTGsgKie1MHun

Merkle Root

7a788bf4926cd4f6d05c064e176133c753c444d0f953fc2338179a3db3a526ee

Transactions (4)

Coinbase0b258ee74dd3d7…58dbba2bc879fe

1 in → 1 out9.0400 XPM109 B

Aaun7Vkj…Kie1MHun

6288814fbd2a4d…d96f68fd2cb29c

154 in → 2 out978.8648 XPM22.33 KB

APXEBRjS…RHnv1rVE AQ8obrRF…hCezsXdr

e2b4ceb4b6900a…03ef8885974fe2

6 in → 2 out285.5632 XPM968 B

AQHE5e6H…xDwU3vYU AcXvBtna…UpJQq8wn

ca81dcee318429…dd4c8da5d14135

1 in → 2 out1.3141 XPM226 B

AJKcLLec…FtUzwmWK AXPo1bBy…VMkpsW1d

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.

2.436 × 10⁹⁶(97-digit number)

24361850841907394948…29739976083892567039

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

2.436 × 10⁹⁶(97-digit number)

24361850841907394948…29739976083892567039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.436 × 10⁹⁶(97-digit number)

24361850841907394948…29739976083892567041

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

4.872 × 10⁹⁶(97-digit number)

48723701683814789897…59479952167785134079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.872 × 10⁹⁶(97-digit number)

48723701683814789897…59479952167785134081

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

9.744 × 10⁹⁶(97-digit number)

97447403367629579794…18959904335570268159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.744 × 10⁹⁶(97-digit number)

97447403367629579794…18959904335570268161

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

1.948 × 10⁹⁷(98-digit number)

19489480673525915958…37919808671140536319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.948 × 10⁹⁷(98-digit number)

19489480673525915958…37919808671140536321

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

3.897 × 10⁹⁷(98-digit number)

38978961347051831917…75839617342281072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.897 × 10⁹⁷(98-digit number)

38978961347051831917…75839617342281072641

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 #1,246,313

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