Block #3,004,979

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/11/2019, 12:56:39 PM · Difficulty 11.2019 · 3,826,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52f2a74143d49a32f4d31f6c4f14b6895606965ac43acea1b5b4b0566a6f74e7

View on Chainz ↗

Height

#3,004,979

Difficulty

11.201863

Transactions

Size

1.90 KB

Version

Bits

0b33ad48

Nonce

745,019,639

Timestamp

1/11/2019, 12:56:39 PM

Confirmations

3,826,123

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f9ac910a0fe7cc6f4f011b3e9b00f1b9f8e5ff2f9676d324cb25af3f79e90b6c

Transactions (4)

Coinbasea76ca86d18f591…7940962b8eb157

1 in → 1 out7.9900 XPM110 B

AbXwmGxD…4XXYP765

b39117ea577db4…9c73c6701abd03

7 in → 2 out50.4279 XPM913 B

AbXwmGxD…4XXYP765 ALdXNNLi…KbXoShEJ

77097809c28801…7866f8fa2813f9

4 in → 2 out20.0811 XPM605 B

AbXwmGxD…4XXYP765 AeTUB2qa…kfnm326q

541b62f5b41477…6909e1eff712fd

1 in → 2 out5.8265 XPM227 B

AXkkuUvH…RnzuS6E1 AbXwmGxD…4XXYP765

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.

4.110 × 10⁹⁶(97-digit number)

41109660924763236593…67562612118034872319

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

4.110 × 10⁹⁶(97-digit number)

41109660924763236593…67562612118034872319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.110 × 10⁹⁶(97-digit number)

41109660924763236593…67562612118034872321

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

8.221 × 10⁹⁶(97-digit number)

82219321849526473187…35125224236069744639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.221 × 10⁹⁶(97-digit number)

82219321849526473187…35125224236069744641

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

1.644 × 10⁹⁷(98-digit number)

16443864369905294637…70250448472139489279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.644 × 10⁹⁷(98-digit number)

16443864369905294637…70250448472139489281

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

3.288 × 10⁹⁷(98-digit number)

32887728739810589275…40500896944278978559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.288 × 10⁹⁷(98-digit number)

32887728739810589275…40500896944278978561

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

6.577 × 10⁹⁷(98-digit number)

65775457479621178550…81001793888557957119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.577 × 10⁹⁷(98-digit number)

65775457479621178550…81001793888557957121

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

1.315 × 10⁹⁸(99-digit number)

13155091495924235710…62003587777115914239

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 #3,004,979

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