Block #331,613

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 11:58:31 AM · Difficulty 10.1686 · 6,495,381 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6dd974eb8dea21696b0e87845dc49443b8ea21e5bc856ae05dfac9d189db02a

View on Chainz ↗

Height

#331,613

Difficulty

10.168563

Transactions

Size

6.99 KB

Version

Bits

0a2b26f4

Nonce

151,487

Timestamp

12/27/2013, 11:58:31 AM

Confirmations

6,495,381

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f0beae5e0c87c65f1d2c3a57d082e8b3b8a3ca3edc8fa98bf51797008f79e323

Transactions (3)

Coinbase2495fe6cb45ae7…1d9e833e20977d

1 in → 1 out9.7300 XPM110 B

AeKNrjNj…1NEq95Ta

0bfe546671b5b9…f211c57b46f50d

6 in → 2 out15.3489 XPM964 B

ALye2TLm…4H9wkuHx AXbiCh58…S7mvDvZG

6e30e61b271bac…608480329ee198

40 in → 2 out40.7836 XPM5.85 KB

AXfoNs1f…6PnV9sEv AREePWUD…CX2zF3mR

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.

3.378 × 10⁹⁸(99-digit number)

33781971382420070906…37506732050998146999

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

3.378 × 10⁹⁸(99-digit number)

33781971382420070906…37506732050998146999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.378 × 10⁹⁸(99-digit number)

33781971382420070906…37506732050998147001

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

6.756 × 10⁹⁸(99-digit number)

67563942764840141813…75013464101996293999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.756 × 10⁹⁸(99-digit number)

67563942764840141813…75013464101996294001

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

1.351 × 10⁹⁹(100-digit number)

13512788552968028362…50026928203992587999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.351 × 10⁹⁹(100-digit number)

13512788552968028362…50026928203992588001

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

2.702 × 10⁹⁹(100-digit number)

27025577105936056725…00053856407985175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.702 × 10⁹⁹(100-digit number)

27025577105936056725…00053856407985176001

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

5.405 × 10⁹⁹(100-digit number)

54051154211872113451…00107712815970351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.405 × 10⁹⁹(100-digit number)

54051154211872113451…00107712815970352001

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 #331,613

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