Block #489,782

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 12:07:51 PM · Difficulty 10.6687 · 6,320,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6faccc2f640dc11e09d6159a7d7e3677684861f41d0257a8fad0f2c5588a33c

View on Chainz ↗

Height

#489,782

Difficulty

10.668660

Transactions

Size

393 B

Version

Bits

0aab2d51

Nonce

14,792,930

Timestamp

4/13/2014, 12:07:51 PM

Confirmations

6,320,071

Mined by

⛏️ P2SHAM4sv2W4Nad5B5XjtfhzJYMGGDPKUoAU4c

Merkle Root

189283f1be409ce8cf90e2f99ef55209caf56b890ac0586378ec09b220bf7b89

Transactions (2)

Coinbase1c32c0be994fae…62c0cc7820c50b

1 in → 1 out8.7800 XPM110 B

AM4sv2W4…PKUoAU4c

e9b71ff5ec31d1…1c11bc54ea9c3c

1 in → 1 out3.0228 XPM191 B

ANDfb1Yy…wpAPTGgt

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.

2.317 × 10¹⁰⁰(101-digit number)

23177052964687759263…21749434676967956479

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

2.317 × 10¹⁰⁰(101-digit number)

23177052964687759263…21749434676967956479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.317 × 10¹⁰⁰(101-digit number)

23177052964687759263…21749434676967956481

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

4.635 × 10¹⁰⁰(101-digit number)

46354105929375518527…43498869353935912959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.635 × 10¹⁰⁰(101-digit number)

46354105929375518527…43498869353935912961

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

9.270 × 10¹⁰⁰(101-digit number)

92708211858751037054…86997738707871825919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.270 × 10¹⁰⁰(101-digit number)

92708211858751037054…86997738707871825921

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

1.854 × 10¹⁰¹(102-digit number)

18541642371750207410…73995477415743651839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.854 × 10¹⁰¹(102-digit number)

18541642371750207410…73995477415743651841

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

3.708 × 10¹⁰¹(102-digit number)

37083284743500414821…47990954831487303679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.708 × 10¹⁰¹(102-digit number)

37083284743500414821…47990954831487303681

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 #489,782

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