Block #2,694,408

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/6/2018, 2:18:13 PM · Difficulty 11.6775 · 4,136,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33c83d2ab86b10d706aa60915f60a2ddc4cea16b109c26bcc18aa15960c5139c

View on Chainz ↗

Height

#2,694,408

Difficulty

11.677508

Transactions

Size

869 B

Version

Bits

0bad7123

Nonce

1,025,358,402

Timestamp

6/6/2018, 2:18:13 PM

Confirmations

4,136,707

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

fb7899317c0657a0e2000778b530275cfc5a5db0029da224ed978bf30c54d497

Transactions (2)

Coinbased0f0f9648633cf…0a7e4d398e333a

1 in → 1 out7.3300 XPM110 B

Adqah8zh…1WwoHJ9t

1065520b59d0fa…92d3e6c58762da

4 in → 2 out5600.0099 XPM668 B

AeMWsReR…6pFxzKmT AecewPGm…iZURiyk8

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.

1.240 × 10⁹⁸(99-digit number)

12405699379786280945…70939057190387711999

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

1.240 × 10⁹⁸(99-digit number)

12405699379786280945…70939057190387711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.240 × 10⁹⁸(99-digit number)

12405699379786280945…70939057190387712001

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

2.481 × 10⁹⁸(99-digit number)

24811398759572561891…41878114380775423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.481 × 10⁹⁸(99-digit number)

24811398759572561891…41878114380775424001

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

4.962 × 10⁹⁸(99-digit number)

49622797519145123783…83756228761550847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.962 × 10⁹⁸(99-digit number)

49622797519145123783…83756228761550848001

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

9.924 × 10⁹⁸(99-digit number)

99245595038290247567…67512457523101695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.924 × 10⁹⁸(99-digit number)

99245595038290247567…67512457523101696001

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

1.984 × 10⁹⁹(100-digit number)

19849119007658049513…35024915046203391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.984 × 10⁹⁹(100-digit number)

19849119007658049513…35024915046203392001

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

3.969 × 10⁹⁹(100-digit number)

39698238015316099027…70049830092406783999

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 #2,694,408

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