Block #491,308

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 10:34:33 AM · Difficulty 10.6806 · 6,335,269 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84e3fa56f707a092f6a8a4776f37cc9751620b9e18c788ab24804c3158ee0bc6

View on Chainz ↗

Height

#491,308

Difficulty

10.680594

Transactions

Size

886 B

Version

Bits

0aae3b63

Nonce

131,650,517

Timestamp

4/14/2014, 10:34:33 AM

Confirmations

6,335,269

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cc3682178bdf5528cbd728f95ca86d199b055db7ab475c42508850154408ac4a

Transactions (4)

Coinbase0f1d95bd2a7481…a6468ade6b7b91

1 in → 1 out8.7800 XPM116 B

AbwWkWZt…kawDhufa

bca169a50555a9…19118f50d99397

1 in → 2 out6.1822 XPM226 B

APLVgC92…3BSA6Zkt AWQLDeMk…e6NnhKFY

ceaf54f2213a7f…3b73ea81a61102

1 in → 2 out3.7214 XPM225 B

Abt4Hmm5…dRTmjvCf AczJNnfo…5jh4mwMK

1fe7503229ea1d…20d8ca0a10438a

1 in → 2 out0.5460 XPM227 B

AUEfgciq…JxYNG9Ty AbKGkHP5…P4yap9Uq

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.

4.471 × 10⁹⁸(99-digit number)

44711580241521877639…85400927605406720959

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

4.471 × 10⁹⁸(99-digit number)

44711580241521877639…85400927605406720959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.471 × 10⁹⁸(99-digit number)

44711580241521877639…85400927605406720961

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

8.942 × 10⁹⁸(99-digit number)

89423160483043755278…70801855210813441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.942 × 10⁹⁸(99-digit number)

89423160483043755278…70801855210813441921

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

1.788 × 10⁹⁹(100-digit number)

17884632096608751055…41603710421626883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.788 × 10⁹⁹(100-digit number)

17884632096608751055…41603710421626883841

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

3.576 × 10⁹⁹(100-digit number)

35769264193217502111…83207420843253767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.576 × 10⁹⁹(100-digit number)

35769264193217502111…83207420843253767681

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

7.153 × 10⁹⁹(100-digit number)

71538528386435004222…66414841686507535359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.153 × 10⁹⁹(100-digit number)

71538528386435004222…66414841686507535361

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 #491,308

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