Block #848,466

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2014, 2:51:36 AM · Difficulty 10.9716 · 5,993,887 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

732bedbd30cb18b22c64f771e0e0d415aba34f15e62e097956cdaf13b8b70b1d

View on Chainz ↗

Height

#848,466

Difficulty

10.971558

Transactions

Size

1.49 KB

Version

Bits

0af8b807

Nonce

669,904,928

Timestamp

12/11/2014, 2:51:36 AM

Confirmations

5,993,887

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cbc0704a5fdea8c4157c1bd7403c186f3c32bad1316de435f1da71457cebc20a

Transactions (5)

Coinbase591fd0c92d674e…1ed7de40727765

1 in → 1 out8.3444 XPM116 B

ANSXnLY2…Sd25TjkD

878da6e55aee5c…9638471df07226

4 in → 2 out20.4178 XPM672 B

AMgiDzC8…poDJoajM AaU9J1Lk…4e47uLfq

2cf651eb4a7337…d80e878f780f29

1 in → 2 out5.6263 XPM227 B

ARpjHv1k…4F9NvuWN AUXgQEwc…XE6KhPcN

a14231b5c48f18…3f8262b90c4da7

1 in → 1 out0.0105 XPM193 B

AUGeGp7y…Zk9J4Ly8

7a46405cd6bdae…05ff9726ecab56

1 in → 2 out0.0974 XPM227 B

AWbMVKmA…viaVeQHQ ARxsB5mz…pHqHUwqr

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.

1.817 × 10⁹⁷(98-digit number)

18172659912087125229…14153274822922403839

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

1.817 × 10⁹⁷(98-digit number)

18172659912087125229…14153274822922403839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.817 × 10⁹⁷(98-digit number)

18172659912087125229…14153274822922403841

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

3.634 × 10⁹⁷(98-digit number)

36345319824174250459…28306549645844807679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.634 × 10⁹⁷(98-digit number)

36345319824174250459…28306549645844807681

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

7.269 × 10⁹⁷(98-digit number)

72690639648348500919…56613099291689615359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.269 × 10⁹⁷(98-digit number)

72690639648348500919…56613099291689615361

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

1.453 × 10⁹⁸(99-digit number)

14538127929669700183…13226198583379230719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.453 × 10⁹⁸(99-digit number)

14538127929669700183…13226198583379230721

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

2.907 × 10⁹⁸(99-digit number)

29076255859339400367…26452397166758461439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.907 × 10⁹⁸(99-digit number)

29076255859339400367…26452397166758461441

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 #848,466

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