Block #2,134,404

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/27/2017, 5:41:23 AM · Difficulty 10.9085 · 4,705,090 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb2104e36f39b06aa8708ccf5935744a309ac2298ec411bc745b4e210b3e5a97

View on Chainz ↗

Height

#2,134,404

Difficulty

10.908547

Transactions

Size

1.07 KB

Version

Bits

0ae8968e

Nonce

460,360,097

Timestamp

5/27/2017, 5:41:23 AM

Confirmations

4,705,090

Mined by

⛏️ P2SHAPzWpkDm8hDCPpKRF34UUo8ULE1ejZt2YA

Merkle Root

71b44aa1c49455545565bc00aa6820f4081f8a571aa075eacfb0248bdf995021

Transactions (3)

Coinbase4a0c2bf2f99839…8f24989a56f8fa

1 in → 1 out8.4100 XPM110 B

APzWpkDm…1ejZt2YA

27040dd4dade0b…509a1db85a2d68

1 in → 2 out174213.9274 XPM226 B

AQwEJfN1…TPxwW8MF ALMPewEv…QkLHqEuW

9683f7f202405c…b31038413b7fc9

4 in → 2 out49.8433 XPM670 B

AUaCaV12…5Eo9Zwtd Ab93GhZb…yWemLsBS

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.

7.768 × 10⁹⁵(96-digit number)

77683098029437410830…76513562710453759999

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

7.768 × 10⁹⁵(96-digit number)

77683098029437410830…76513562710453759999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.768 × 10⁹⁵(96-digit number)

77683098029437410830…76513562710453760001

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

1.553 × 10⁹⁶(97-digit number)

15536619605887482166…53027125420907519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.553 × 10⁹⁶(97-digit number)

15536619605887482166…53027125420907520001

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

3.107 × 10⁹⁶(97-digit number)

31073239211774964332…06054250841815039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.107 × 10⁹⁶(97-digit number)

31073239211774964332…06054250841815040001

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

6.214 × 10⁹⁶(97-digit number)

62146478423549928664…12108501683630079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.214 × 10⁹⁶(97-digit number)

62146478423549928664…12108501683630080001

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

1.242 × 10⁹⁷(98-digit number)

12429295684709985732…24217003367260159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.242 × 10⁹⁷(98-digit number)

12429295684709985732…24217003367260160001

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 #2,134,404

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