Block #2,946,104

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/30/2018, 3:54:51 PM · Difficulty 11.3965 · 3,887,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35e6bb0e99e2b068952de4e0003756dd80e61cf268e0b11f804d0fb4903ed895

View on Chainz ↗

Height

#2,946,104

Difficulty

11.396525

Transactions

Size

199 B

Version

Bits

0b6582aa

Nonce

984,494,079

Timestamp

11/30/2018, 3:54:51 PM

Confirmations

3,887,221

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

df3b0ebeb6fb4e491f2dc502c6c4ed2f3cb31d9cb608ae58a51f442d09c10967

Transactions (1)

Coinbasedf3b0ebeb6fb4e…1f442d09c10967

1 in → 1 out7.6900 XPM110 B

AUMQRepm…tAfKmdW1

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.

2.439 × 10⁹¹(92-digit number)

24399055422223542672…22566887023254840579

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

2.439 × 10⁹¹(92-digit number)

24399055422223542672…22566887023254840579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.439 × 10⁹¹(92-digit number)

24399055422223542672…22566887023254840581

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

4.879 × 10⁹¹(92-digit number)

48798110844447085345…45133774046509681159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.879 × 10⁹¹(92-digit number)

48798110844447085345…45133774046509681161

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

9.759 × 10⁹¹(92-digit number)

97596221688894170690…90267548093019362319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.759 × 10⁹¹(92-digit number)

97596221688894170690…90267548093019362321

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

1.951 × 10⁹²(93-digit number)

19519244337778834138…80535096186038724639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.951 × 10⁹²(93-digit number)

19519244337778834138…80535096186038724641

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

3.903 × 10⁹²(93-digit number)

39038488675557668276…61070192372077449279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.903 × 10⁹²(93-digit number)

39038488675557668276…61070192372077449281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.807 × 10⁹²(93-digit number)

78076977351115336552…22140384744154898559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,946,104

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