Block #323,185

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 11:51:29 AM · Difficulty 10.2020 · 6,490,827 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0cef5d4e82a094950b5aad3f60e1049f01caf2bf368b778af042688ea3cb973

View on Chainz ↗

Height

#323,185

Difficulty

10.202026

Transactions

Size

1.68 KB

Version

Bits

0a33b7fc

Nonce

17,778

Timestamp

12/21/2013, 11:51:29 AM

Confirmations

6,490,827

Mined by

⛏️ qaR5Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

eeab3e430b166f9132702db2c47cb5bf9e04d162b576406f2c350d4fafd12a42

Transactions (4)

Coinbasee1399d4f7075e6…9fbe5ac9b56fa7

1 in → 26 out9.5888 XPM947 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AMJvLrYM…6sSq25D9 AT3ATVPt…Qw6x41k1

c598b862588ea8…4edc3fe98087a4

1 in → 2 out9.6300 XPM227 B

AGWtVz76…kbdYi19h ANYDwWEE…xzEmCjTK

60020754228197…0a1bb4d180c925

1 in → 2 out9.6300 XPM225 B

APS4PAas…U6aXoPX5 ATpoLefg…v7x8Z5Dr

ca13e187b87bc7…479a3e314181a4

1 in → 2 out9.6300 XPM227 B

AeUmG86v…8BGZ7fKS AbEsYBJY…cWkhrGou

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.

5.529 × 10⁹⁷(98-digit number)

55294843276294987980…03432954171115324639

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

5.529 × 10⁹⁷(98-digit number)

55294843276294987980…03432954171115324639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.529 × 10⁹⁷(98-digit number)

55294843276294987980…03432954171115324641

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

1.105 × 10⁹⁸(99-digit number)

11058968655258997596…06865908342230649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.105 × 10⁹⁸(99-digit number)

11058968655258997596…06865908342230649281

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

2.211 × 10⁹⁸(99-digit number)

22117937310517995192…13731816684461298559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.211 × 10⁹⁸(99-digit number)

22117937310517995192…13731816684461298561

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

4.423 × 10⁹⁸(99-digit number)

44235874621035990384…27463633368922597119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.423 × 10⁹⁸(99-digit number)

44235874621035990384…27463633368922597121

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

8.847 × 10⁹⁸(99-digit number)

88471749242071980768…54927266737845194239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.847 × 10⁹⁸(99-digit number)

88471749242071980768…54927266737845194241

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 #323,185

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