Block #3,040,816

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/6/2019, 3:40:48 AM · Difficulty 11.0195 · 3,801,127 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de642e189c2e3423221e175400011c764ee4273d4493f77732d36ebf17a9d9db

View on Chainz ↗

Height

#3,040,816

Difficulty

11.019481

Transactions

Size

1.14 KB

Version

Bits

0b04fcad

Nonce

1,116,613,214

Timestamp

2/6/2019, 3:40:48 AM

Confirmations

3,801,127

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

782f17892402af02b837f106b664b444797e2c5971240522d8d596e1be61c624

Transactions (2)

Coinbase8306a01f29deee…7341ddb00b96f6

1 in → 1 out8.2300 XPM109 B

AUMQRepm…tAfKmdW1

648bb944840a76…7554e84b1ba22a

6 in → 2 out367.2640 XPM965 B

AbzALusA…mujehDd4 AdjinC4o…wZE842K3

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.

5.016 × 10⁹⁵(96-digit number)

50168781935314615112…88044985376903249919

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

5.016 × 10⁹⁵(96-digit number)

50168781935314615112…88044985376903249919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.016 × 10⁹⁵(96-digit number)

50168781935314615112…88044985376903249921

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

1.003 × 10⁹⁶(97-digit number)

10033756387062923022…76089970753806499839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.003 × 10⁹⁶(97-digit number)

10033756387062923022…76089970753806499841

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

2.006 × 10⁹⁶(97-digit number)

20067512774125846044…52179941507612999679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.006 × 10⁹⁶(97-digit number)

20067512774125846044…52179941507612999681

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

4.013 × 10⁹⁶(97-digit number)

40135025548251692089…04359883015225999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.013 × 10⁹⁶(97-digit number)

40135025548251692089…04359883015225999361

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

8.027 × 10⁹⁶(97-digit number)

80270051096503384179…08719766030451998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.027 × 10⁹⁶(97-digit number)

80270051096503384179…08719766030451998721

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

1.605 × 10⁹⁷(98-digit number)

16054010219300676835…17439532060903997439

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 #3,040,816

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