Block #2,067,143

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2017, 3:00:17 AM · Difficulty 10.8529 · 4,759,179 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f5bb31f4bce2ced98cd4b314a07a7ec7c35e46b83ce89146a1bf95dc3477189

View on Chainz ↗

Height

#2,067,143

Difficulty

10.852932

Transactions

Size

64.00 KB

Version

Bits

0ada59c1

Nonce

463,839,108

Timestamp

4/12/2017, 3:00:17 AM

Confirmations

4,759,179

Mined by

⛏️ P2SHAY3ZEgTrPRhu5b6DqBKdWzn3ExECWahbCc

Merkle Root

27cf0307fc4fd7fa4273c1d57dbf1ec9b4a4f1044da51170418dca22bc9d6b95

Transactions (2)

Coinbase847f56a1fa834c…7ac04886e8161b

1 in → 1 out9.1400 XPM110 B

AY3ZEgTr…ECWahbCc

f52d1e442ce88d…e660f8c8481ec5

441 in → 2 out200000.0101 XPM63.80 KB

AKAHKtud…mQBq4Q8J AVtvZgRh…c2KQYDJR

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.

9.331 × 10⁹⁴(95-digit number)

93313998929029700885…84603400563865449679

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

9.331 × 10⁹⁴(95-digit number)

93313998929029700885…84603400563865449679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.331 × 10⁹⁴(95-digit number)

93313998929029700885…84603400563865449681

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

1.866 × 10⁹⁵(96-digit number)

18662799785805940177…69206801127730899359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.866 × 10⁹⁵(96-digit number)

18662799785805940177…69206801127730899361

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

3.732 × 10⁹⁵(96-digit number)

37325599571611880354…38413602255461798719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.732 × 10⁹⁵(96-digit number)

37325599571611880354…38413602255461798721

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

7.465 × 10⁹⁵(96-digit number)

74651199143223760708…76827204510923597439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.465 × 10⁹⁵(96-digit number)

74651199143223760708…76827204510923597441

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

1.493 × 10⁹⁶(97-digit number)

14930239828644752141…53654409021847194879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.493 × 10⁹⁶(97-digit number)

14930239828644752141…53654409021847194881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,067,143

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