Block #114,353

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 2:18:41 AM · Difficulty 9.7394 · 6,693,220 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

520b2a56200f57be7d874432c00828b3546e010dc64b4955ad4d115e38478dc0

View on Chainz ↗

Height

#114,353

Difficulty

9.739415

Transactions

Size

2.34 KB

Version

Bits

09bd4a49

Nonce

491,908

Timestamp

8/13/2013, 2:18:41 AM

Confirmations

6,693,220

Mined by

⛏️ P2SHAWd66mBviifi7tHpuNWe49KvSmsLE9bdaQ

Merkle Root

31c6621aca1e164476c2f7549d1035639bc230c7e22ae47c9612d2074f955927

Transactions (3)

Coinbase657998b191d39b…a5d2329e86d99d

1 in → 1 out10.5600 XPM109 B

AWd66mBv…sLE9bdaQ

a1c10d4bc0e38e…e07584caf9f4eb

3 in → 1 out547.0700 XPM489 B

AFqDj4vn…D3w8GBCw

d24fa583da5a59…02ef59227b4439

11 in → 2 out50.4017 XPM1.67 KB

AWmkbHZV…P3ZTZnwm AbmByNE3…ScrLa5D1

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.

4.854 × 10¹⁰¹(102-digit number)

48547323701910634104…45127537789154697919

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

4.854 × 10¹⁰¹(102-digit number)

48547323701910634104…45127537789154697919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.854 × 10¹⁰¹(102-digit number)

48547323701910634104…45127537789154697921

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

9.709 × 10¹⁰¹(102-digit number)

97094647403821268208…90255075578309395839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.709 × 10¹⁰¹(102-digit number)

97094647403821268208…90255075578309395841

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

1.941 × 10¹⁰²(103-digit number)

19418929480764253641…80510151156618791679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.941 × 10¹⁰²(103-digit number)

19418929480764253641…80510151156618791681

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

3.883 × 10¹⁰²(103-digit number)

38837858961528507283…61020302313237583359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.883 × 10¹⁰²(103-digit number)

38837858961528507283…61020302313237583361

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

7.767 × 10¹⁰²(103-digit number)

77675717923057014567…22040604626475166719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #114,353

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