Block #2,623,281

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/21/2018, 6:30:40 AM · Difficulty 11.2193 · 4,216,395 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bab19359429bf6f196581ab30faa9f2a7f3b4f1e383a35aea3c72d87d1f9ed7c

View on Chainz ↗

Height

#2,623,281

Difficulty

11.219258

Transactions

Size

199 B

Version

Bits

0b382143

Nonce

1,529,654,068

Timestamp

4/21/2018, 6:30:40 AM

Confirmations

4,216,395

Mined by

⛏️ P2SHAT9gytRPiUEVus7JrxUdZv8pFPfhtGYm6h

Merkle Root

d38284b504a27f52c7ac62d8f28528ebbd1253ddfdeed6c989829c309f8c1c0d

Transactions (1)

Coinbased38284b504a27f…829c309f8c1c0d

1 in → 1 out7.9300 XPM109 B

AT9gytRP…fhtGYm6h

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.

3.442 × 10⁹⁵(96-digit number)

34425587512480505297…67821808665414443519

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

3.442 × 10⁹⁵(96-digit number)

34425587512480505297…67821808665414443519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.442 × 10⁹⁵(96-digit number)

34425587512480505297…67821808665414443521

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

6.885 × 10⁹⁵(96-digit number)

68851175024961010594…35643617330828887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.885 × 10⁹⁵(96-digit number)

68851175024961010594…35643617330828887041

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

1.377 × 10⁹⁶(97-digit number)

13770235004992202118…71287234661657774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.377 × 10⁹⁶(97-digit number)

13770235004992202118…71287234661657774081

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

2.754 × 10⁹⁶(97-digit number)

27540470009984404237…42574469323315548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.754 × 10⁹⁶(97-digit number)

27540470009984404237…42574469323315548161

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

5.508 × 10⁹⁶(97-digit number)

55080940019968808475…85148938646631096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.508 × 10⁹⁶(97-digit number)

55080940019968808475…85148938646631096321

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.101 × 10⁹⁷(98-digit number)

11016188003993761695…70297877293262192639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,623,281

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