Block #1,458,099

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2016, 1:05:45 PM · Difficulty 10.7614 · 5,358,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

298d2d6ba4b76e55a7c50631a6448c9338b02f685a49834ab10dcc0235e0e41b

View on Chainz ↗

Height

#1,458,099

Difficulty

10.761385

Transactions

Size

1.01 KB

Version

Bits

0ac2ea28

Nonce

18,226,663

Timestamp

2/15/2016, 1:05:45 PM

Confirmations

5,358,208

Mined by

⛏️ P2SHAVBH1xLXLt8FdHxHu2svghiiobgu1D5qVP

Merkle Root

195bf0beb773113f29716863a26f1eca6819ae045ac74df561356527456d1e59

Transactions (2)

Coinbase78d56cb5187e16…09724dfa99d85e

1 in → 1 out8.6300 XPM109 B

AVBH1xLX…gu1D5qVP

9f289137e3ed9a…860d1364dc80ef

1 in → 20 out31.6277 XPM838 B

AcU7DAK9…XaHQ2hmC AHZEoBHn…uFKevpPQ Ad2a9Y4o…dCd7URGB AR948gVq…y7uqPqsK AMjum32j…okZzjP2A

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.

9.206 × 10⁹⁶(97-digit number)

92063692969040809881…62626509954487173119

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

9.206 × 10⁹⁶(97-digit number)

92063692969040809881…62626509954487173119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.206 × 10⁹⁶(97-digit number)

92063692969040809881…62626509954487173121

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

1.841 × 10⁹⁷(98-digit number)

18412738593808161976…25253019908974346239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.841 × 10⁹⁷(98-digit number)

18412738593808161976…25253019908974346241

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

3.682 × 10⁹⁷(98-digit number)

36825477187616323952…50506039817948692479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.682 × 10⁹⁷(98-digit number)

36825477187616323952…50506039817948692481

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

7.365 × 10⁹⁷(98-digit number)

73650954375232647904…01012079635897384959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.365 × 10⁹⁷(98-digit number)

73650954375232647904…01012079635897384961

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

1.473 × 10⁹⁸(99-digit number)

14730190875046529580…02024159271794769919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.473 × 10⁹⁸(99-digit number)

14730190875046529580…02024159271794769921

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 #1,458,099

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