Block #3,046,821

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/10/2019, 10:14:00 AM · Difficulty 10.9961 · 3,789,765 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b260cad67dc2a231b17ac8c7555e4844ae1013f96e86f835fae8bbeaeab22857

View on Chainz ↗

Height

#3,046,821

Difficulty

10.996091

Transactions

Size

1.68 KB

Version

Bits

0afeffcc

Nonce

509,049,037

Timestamp

2/10/2019, 10:14:00 AM

Confirmations

3,789,765

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

080512f6bc79781dc2a191a4d65e0766209c1480c1bd3c72debb0f0f0ea34154

Transactions (2)

Coinbasef5a43d47b08490…0d8822a6401111

1 in → 1 out8.2900 XPM109 B

AUMQRepm…tAfKmdW1

1ad462e3e9a09d…b97359d4a46aec

10 in → 1 out1985.0882 XPM1.49 KB

ARo9Bx54…mTopc3JB

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.

1.013 × 10⁹³(94-digit number)

10137503239749436519…03750103820297408649

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

1.013 × 10⁹³(94-digit number)

10137503239749436519…03750103820297408649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.013 × 10⁹³(94-digit number)

10137503239749436519…03750103820297408651

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

2.027 × 10⁹³(94-digit number)

20275006479498873039…07500207640594817299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.027 × 10⁹³(94-digit number)

20275006479498873039…07500207640594817301

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

4.055 × 10⁹³(94-digit number)

40550012958997746079…15000415281189634599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.055 × 10⁹³(94-digit number)

40550012958997746079…15000415281189634601

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

8.110 × 10⁹³(94-digit number)

81100025917995492158…30000830562379269199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.110 × 10⁹³(94-digit number)

81100025917995492158…30000830562379269201

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

1.622 × 10⁹⁴(95-digit number)

16220005183599098431…60001661124758538399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.622 × 10⁹⁴(95-digit number)

16220005183599098431…60001661124758538401

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

3.244 × 10⁹⁴(95-digit number)

32440010367198196863…20003322249517076799

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 #3,046,821

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