Block #1,492,997

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2016, 10:06:37 PM · Difficulty 10.6711 · 5,350,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

749746b8784dcd7695d866cc304ead177c54e7e6160c5f92ea3296c9c5a0decf

View on Chainz ↗

Height

#1,492,997

Difficulty

10.671106

Transactions

Size

1.08 KB

Version

Bits

0aabcd93

Nonce

1,294,923,310

Timestamp

3/11/2016, 10:06:37 PM

Confirmations

5,350,287

Mined by

⛏️ P2SHANCUVxyNWkEQ2DQM3i1mwRmx1K3h2VZ8xp

Merkle Root

ddf14bd3331ecb14ded0c2c1ed8ae5e15a9817741ad06d2f787c3f9941bb914c

Transactions (2)

Coinbase649336f5443a5f…415f17a36f2969

1 in → 1 out8.7800 XPM109 B

ANCUVxyN…3h2VZ8xp

9031005b4b5b87…436ffcf82bbacd

1 in → 22 out171.6781 XPM906 B

Ae9wYuZx…WqNFE1D7 ALckfvnf…kcCn1c1R Aa2PYG8E…enqokkbR AdNsYf3e…oT7bWNLb AJEvwCTe…BAeaMBAe

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.

1.224 × 10⁹⁵(96-digit number)

12248475241764580610…71364132278033941599

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

1.224 × 10⁹⁵(96-digit number)

12248475241764580610…71364132278033941599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.224 × 10⁹⁵(96-digit number)

12248475241764580610…71364132278033941601

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

2.449 × 10⁹⁵(96-digit number)

24496950483529161220…42728264556067883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.449 × 10⁹⁵(96-digit number)

24496950483529161220…42728264556067883201

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

4.899 × 10⁹⁵(96-digit number)

48993900967058322440…85456529112135766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.899 × 10⁹⁵(96-digit number)

48993900967058322440…85456529112135766401

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

9.798 × 10⁹⁵(96-digit number)

97987801934116644881…70913058224271532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.798 × 10⁹⁵(96-digit number)

97987801934116644881…70913058224271532801

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

1.959 × 10⁹⁶(97-digit number)

19597560386823328976…41826116448543065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.959 × 10⁹⁶(97-digit number)

19597560386823328976…41826116448543065601

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 #1,492,997

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