Block #1,906,162

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2016, 6:16:01 PM · Difficulty 10.7715 · 4,936,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f50a8ecb3710ffa80a104838586404716dc3dea982a62b8050a1deb45e34e365

View on Chainz ↗

Height

#1,906,162

Difficulty

10.771452

Transactions

Size

868 B

Version

Bits

0ac57ddc

Nonce

2,024,717,610

Timestamp

12/22/2016, 6:16:01 PM

Confirmations

4,936,137

Mined by

⛏️ P2SHAZwQGXNfKqbEBXyM5sX5HZtMNh2bnH116p

Merkle Root

8d45c2cbd03da1f9fe6b40e1127c6d18089acb4228a292d5b07b92537569042b

Transactions (2)

Coinbase19640590eeceba…dcc096f5d595ec

1 in → 1 out8.6200 XPM109 B

AZwQGXNf…2bnH116p

b9f473e74ddc90…3b0c9ad12cd49f

4 in → 2 out1.0100 XPM668 B

AeayPRPN…ytw57suU ALPML9a6…s42GnBFV

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.

1.913 × 10⁹⁷(98-digit number)

19130734965538346445…19417266921336831999

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

1.913 × 10⁹⁷(98-digit number)

19130734965538346445…19417266921336831999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.913 × 10⁹⁷(98-digit number)

19130734965538346445…19417266921336832001

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

3.826 × 10⁹⁷(98-digit number)

38261469931076692890…38834533842673663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.826 × 10⁹⁷(98-digit number)

38261469931076692890…38834533842673664001

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

7.652 × 10⁹⁷(98-digit number)

76522939862153385781…77669067685347327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.652 × 10⁹⁷(98-digit number)

76522939862153385781…77669067685347328001

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

1.530 × 10⁹⁸(99-digit number)

15304587972430677156…55338135370694655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.530 × 10⁹⁸(99-digit number)

15304587972430677156…55338135370694656001

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

3.060 × 10⁹⁸(99-digit number)

30609175944861354312…10676270741389311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.060 × 10⁹⁸(99-digit number)

30609175944861354312…10676270741389312001

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 #1,906,162

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