Block #322,246

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 8:34:26 PM · Difficulty 10.1986 · 6,503,465 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0fc1b6d772d2626b7f7235f6c930c77f594e46077ccc5591267620b3f5313251

View on Chainz ↗

Height

#322,246

Difficulty

10.198584

Transactions

Size

1.82 KB

Version

Bits

0a32d668

Nonce

60,299

Timestamp

12/20/2013, 8:34:26 PM

Confirmations

6,503,465

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

f330245dda9be5c05b251af5b243dd70f35bb3634da5b060154f2f26034d7a30

Transactions (4)

Coinbase27663977441a2a…5925839dd7eeca

1 in → 26 out9.6000 XPM947 B

Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AYcLTeXR…bscgPops

45efe1720a2029…2676a9abe2dbb8

2 in → 2 out5.0812 XPM376 B

AGahrAsw…jLmDizDK AN7S5zd5…nEf6mAqg

0680781144985d…2707ed2e7d32b5

1 in → 2 out12.4900 XPM225 B

AJtcYzHf…A1nq73qL AcDPdBKV…qLMcdY5a

9190a8bb403b4d…d3ab0eb3422178

1 in → 2 out4.4833 XPM226 B

Aa116rAs…LcTBfcoi AJHMeUzo…o5EQTvMg

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.

1.790 × 10⁹⁵(96-digit number)

17902411923022900995…27374838323051379699

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

1.790 × 10⁹⁵(96-digit number)

17902411923022900995…27374838323051379699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.790 × 10⁹⁵(96-digit number)

17902411923022900995…27374838323051379701

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

3.580 × 10⁹⁵(96-digit number)

35804823846045801991…54749676646102759399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.580 × 10⁹⁵(96-digit number)

35804823846045801991…54749676646102759401

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

7.160 × 10⁹⁵(96-digit number)

71609647692091603983…09499353292205518799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.160 × 10⁹⁵(96-digit number)

71609647692091603983…09499353292205518801

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

1.432 × 10⁹⁶(97-digit number)

14321929538418320796…18998706584411037599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.432 × 10⁹⁶(97-digit number)

14321929538418320796…18998706584411037601

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

2.864 × 10⁹⁶(97-digit number)

28643859076836641593…37997413168822075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.864 × 10⁹⁶(97-digit number)

28643859076836641593…37997413168822075201

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 #322,246

Cookie Preferences