Block #3,005,306

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/11/2019, 6:32:34 PM · Difficulty 11.2009 · 3,836,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5623713cfb4463ff4e7279ac1636ec5299bc56c28e5bcb07012198c6887d698

View on Chainz ↗

Height

#3,005,306

Difficulty

11.200897

Transactions

Size

845 B

Version

Bits

0b336e04

Nonce

522,346,294

Timestamp

1/11/2019, 6:32:34 PM

Confirmations

3,836,791

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

2bc26ca54e614bdb6b00771f3273ff69208d7b3a133538612046658a5ad360bc

Transactions (3)

Coinbase3f5dcb5a185a6d…167ab39d8d6c1b

1 in → 1 out7.9800 XPM109 B

AUhjokok…k5m93PZR

982816de0412cc…d81df82792f06c

2 in → 2 out15.9000 XPM305 B

ANiRSGwW…LtXULkMk Acjq27Rf…KjmPjf78

14ed0877eba3f3…2dd6f7292bba5d

2 in → 2 out11.7700 XPM341 B

AaHsEQd6…A22sKQ7o AckbU51J…6byYVKuR

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.

1.916 × 10⁹⁴(95-digit number)

19161255237039476014…12238886128311162879

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

1.916 × 10⁹⁴(95-digit number)

19161255237039476014…12238886128311162879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.916 × 10⁹⁴(95-digit number)

19161255237039476014…12238886128311162881

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

3.832 × 10⁹⁴(95-digit number)

38322510474078952028…24477772256622325759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.832 × 10⁹⁴(95-digit number)

38322510474078952028…24477772256622325761

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

7.664 × 10⁹⁴(95-digit number)

76645020948157904056…48955544513244651519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.664 × 10⁹⁴(95-digit number)

76645020948157904056…48955544513244651521

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

1.532 × 10⁹⁵(96-digit number)

15329004189631580811…97911089026489303039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.532 × 10⁹⁵(96-digit number)

15329004189631580811…97911089026489303041

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

3.065 × 10⁹⁵(96-digit number)

30658008379263161622…95822178052978606079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.065 × 10⁹⁵(96-digit number)

30658008379263161622…95822178052978606081

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

6.131 × 10⁹⁵(96-digit number)

61316016758526323245…91644356105957212159

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 #3,005,306

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