Block #2,929,744

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/19/2018, 8:43:34 AM · Difficulty 11.3853 · 3,915,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c49c506b2d98ecc8e5376833d7d214887255ea8813d15ad20e394ec5fc5ab27a

View on Chainz ↗

Height

#2,929,744

Difficulty

11.385284

Transactions

Size

755 B

Version

Bits

0b62a1f8

Nonce

1,297,068,173

Timestamp

11/19/2018, 8:43:34 AM

Confirmations

3,915,246

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

347aa721e7363bf9c00d369b47c0a3da32399f68d53d2c5ea8f8e2e7598e52ec

Transactions (2)

Coinbase0394cdbb3660b8…0ef76ef648e7ab

1 in → 1 out7.7100 XPM109 B

AbXwmGxD…4XXYP765

71fd002ed40e70…26efbabe7e097f

3 in → 3 out477.7188 XPM557 B

AXsr1Tzj…WpYKVnB4 AeE8jzQC…xaMsk2EK AeoYRFM9…akPhgXp7

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.

3.768 × 10⁹¹(92-digit number)

37682789715008337686…12021161933396048639

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

3.768 × 10⁹¹(92-digit number)

37682789715008337686…12021161933396048639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.768 × 10⁹¹(92-digit number)

37682789715008337686…12021161933396048641

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

7.536 × 10⁹¹(92-digit number)

75365579430016675372…24042323866792097279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.536 × 10⁹¹(92-digit number)

75365579430016675372…24042323866792097281

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

1.507 × 10⁹²(93-digit number)

15073115886003335074…48084647733584194559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.507 × 10⁹²(93-digit number)

15073115886003335074…48084647733584194561

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

3.014 × 10⁹²(93-digit number)

30146231772006670148…96169295467168389119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.014 × 10⁹²(93-digit number)

30146231772006670148…96169295467168389121

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

6.029 × 10⁹²(93-digit number)

60292463544013340297…92338590934336778239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.029 × 10⁹²(93-digit number)

60292463544013340297…92338590934336778241

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

1.205 × 10⁹³(94-digit number)

12058492708802668059…84677181868673556479

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 #2,929,744

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