Block #2,826,939

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/6/2018, 7:18:46 AM · Difficulty 11.7100 · 4,013,007 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ee329983e37dde477e04402d608239cbfa3209eeb9357dd33cfc446fb1e5ae3

View on Chainz ↗

Height

#2,826,939

Difficulty

11.710022

Transactions

Size

201 B

Version

Bits

0bb5c407

Nonce

348,915,242

Timestamp

9/6/2018, 7:18:46 AM

Confirmations

4,013,007

Mined by

⛏️ P2SHAe9bd5ZsNbgz9tUCsvWce7vXTGi1E3D1Ae

Merkle Root

08d871bbcd93bcf625d1cd792ec8a1c050af67f39a3d1d31d9d8664b15b8c787

Transactions (1)

Coinbase08d871bbcd93bc…d8664b15b8c787

1 in → 1 out7.2800 XPM110 B

Ae9bd5Zs…i1E3D1Ae

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.

7.951 × 10⁹⁵(96-digit number)

79510836716654282345…20849198377703331839

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

7.951 × 10⁹⁵(96-digit number)

79510836716654282345…20849198377703331839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.951 × 10⁹⁵(96-digit number)

79510836716654282345…20849198377703331841

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

1.590 × 10⁹⁶(97-digit number)

15902167343330856469…41698396755406663679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.590 × 10⁹⁶(97-digit number)

15902167343330856469…41698396755406663681

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

3.180 × 10⁹⁶(97-digit number)

31804334686661712938…83396793510813327359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.180 × 10⁹⁶(97-digit number)

31804334686661712938…83396793510813327361

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

6.360 × 10⁹⁶(97-digit number)

63608669373323425876…66793587021626654719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.360 × 10⁹⁶(97-digit number)

63608669373323425876…66793587021626654721

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

1.272 × 10⁹⁷(98-digit number)

12721733874664685175…33587174043253309439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.272 × 10⁹⁷(98-digit number)

12721733874664685175…33587174043253309441

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

2.544 × 10⁹⁷(98-digit number)

25443467749329370350…67174348086506618879

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 #2,826,939

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