Block #341,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 6:24:02 PM · Difficulty 10.1487 · 6,467,922 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2eeee513b78876e7ed2e7bafe90c713825379162bf7567af758b13834d314bdf

View on Chainz ↗

Height

#341,936

Difficulty

10.148744

Transactions

Size

1.14 KB

Version

Bits

0a26141e

Nonce

273,400

Timestamp

1/3/2014, 6:24:02 PM

Confirmations

6,467,922

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8550e8e27a2d5b27662ae60df1ea4bae5869bad51e04ea452804e6736eaf1ec7

Transactions (2)

Coinbase0b0b39e43a1ff4…323d864c569a82

1 in → 1 out9.7000 XPM110 B

AeKNrjNj…1NEq95Ta

24da02d9b349b6…fa9678d478ce59

6 in → 2 out49.9324 XPM967 B

APyFpZ1p…6e3r8Vq9 AKGLdGPV…v8MmKBfG

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.

1.673 × 10⁹⁹(100-digit number)

16731619331900657815…29487884478047303579

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

1.673 × 10⁹⁹(100-digit number)

16731619331900657815…29487884478047303579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.673 × 10⁹⁹(100-digit number)

16731619331900657815…29487884478047303581

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

3.346 × 10⁹⁹(100-digit number)

33463238663801315630…58975768956094607159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.346 × 10⁹⁹(100-digit number)

33463238663801315630…58975768956094607161

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

6.692 × 10⁹⁹(100-digit number)

66926477327602631260…17951537912189214319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.692 × 10⁹⁹(100-digit number)

66926477327602631260…17951537912189214321

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

1.338 × 10¹⁰⁰(101-digit number)

13385295465520526252…35903075824378428639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.338 × 10¹⁰⁰(101-digit number)

13385295465520526252…35903075824378428641

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

2.677 × 10¹⁰⁰(101-digit number)

26770590931041052504…71806151648756857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.677 × 10¹⁰⁰(101-digit number)

26770590931041052504…71806151648756857281

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 #341,936

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