Block #455,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 6:58:46 PM · Difficulty 10.4172 · 6,350,278 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ca95ff08fe88426463667aedcc8a6c8937949216a4f489e2e825cafd6d98a84

View on Chainz ↗

Height

#455,812

Difficulty

10.417191

Transactions

Size

1.60 KB

Version

Bits

0a6acd00

Nonce

112,933

Timestamp

3/22/2014, 6:58:46 PM

Confirmations

6,350,278

Mined by

AN9emqpK7dgr5Ubo53Xd9AuJhzWEnrfX7s

Merkle Root

2047a9b45fa4169966c43ad5505402a88d3a9f000f9a76124450b8160829f50d

Transactions (5)

Coinbasedf190e05e6c0f2…09e8a01b625335

1 in → 5 out9.2400 XPM233 B

AN9emqpK…WEnrfX7s AHQyfiZn…sQbeqE98 AWCjgrw2…MnFAU7HX ARJu9Qoh…JpP9irBQ AZzi9Hj6…PuNWYX6G

6be1b93999e0de…89eaf97863d13c

1 in → 5 out35.9660 XPM327 B

AUoAjuAg…oYcX3CJZ AQe12e3Z…HeWcXVsQ ASkFo4Us…CnRy9vHn AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt

0c87e03fe08680…9a2169e6095890

1 in → 5 out20.9658 XPM329 B

AUoAjuAg…oYcX3CJZ AJiUWmxX…BMH9Vzvt AYmXDTRZ…RjoLiimC ATTYFZme…MSmQSMWm AQe12e3Z…HeWcXVsQ

c3385997108616…f0446a83a9bbfc

1 in → 5 out11.9564 XPM327 B

AcjxMFNY…XTPwBYU9 AYmXDTRZ…RjoLiimC AUoAjuAg…oYcX3CJZ AJiUWmxX…BMH9Vzvt AG9SfhhW…sSJdWcrQ

277fe780294012…248bb57c659468

1 in → 5 out35.9659 XPM328 B

AUoAjuAg…oYcX3CJZ AbXLhPPh…WpESmUtE AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ AYmXDTRZ…RjoLiimC

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.

5.156 × 10⁹⁷(98-digit number)

51565772390788390537…92743260809892746239

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

5.156 × 10⁹⁷(98-digit number)

51565772390788390537…92743260809892746239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.156 × 10⁹⁷(98-digit number)

51565772390788390537…92743260809892746241

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

1.031 × 10⁹⁸(99-digit number)

10313154478157678107…85486521619785492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.031 × 10⁹⁸(99-digit number)

10313154478157678107…85486521619785492481

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

2.062 × 10⁹⁸(99-digit number)

20626308956315356215…70973043239570984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.062 × 10⁹⁸(99-digit number)

20626308956315356215…70973043239570984961

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

4.125 × 10⁹⁸(99-digit number)

41252617912630712430…41946086479141969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.125 × 10⁹⁸(99-digit number)

41252617912630712430…41946086479141969921

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

8.250 × 10⁹⁸(99-digit number)

82505235825261424860…83892172958283939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.250 × 10⁹⁸(99-digit number)

82505235825261424860…83892172958283939841

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