Block #181,403

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/26/2013, 1:23:27 PM · Difficulty 9.8597 · 6,610,406 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b08edc2cfd936ff76f730d1d458aadaddd5fd5f5a6a00cfbbdd635f67a68863f

View on Chainz ↗

Height

#181,403

Difficulty

9.859743

Transactions

Size

197 B

Version

Bits

09dc181b

Nonce

24,617

Timestamp

9/26/2013, 1:23:27 PM

Confirmations

6,610,406

Merkle Root

566fb0a3d5b68a94ebed06e01d753a6569d46220514d3217d8f2dd23c9494b3d

Transactions (1)

Coinbase566fb0a3d5b68a…f2dd23c9494b3d

1 in → 1 out10.2700 XPM109 B

AKhaGKFX…KjeAXtBv

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.

7.210 × 10⁸⁹(90-digit number)

72108939918681174249…24883800145523822759

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

7.210 × 10⁸⁹(90-digit number)

72108939918681174249…24883800145523822759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.210 × 10⁸⁹(90-digit number)

72108939918681174249…24883800145523822761

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

1.442 × 10⁹⁰(91-digit number)

14421787983736234849…49767600291047645519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.442 × 10⁹⁰(91-digit number)

14421787983736234849…49767600291047645521

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

2.884 × 10⁹⁰(91-digit number)

28843575967472469699…99535200582095291039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.884 × 10⁹⁰(91-digit number)

28843575967472469699…99535200582095291041

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

5.768 × 10⁹⁰(91-digit number)

57687151934944939399…99070401164190582079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.768 × 10⁹⁰(91-digit number)

57687151934944939399…99070401164190582081

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

1.153 × 10⁹¹(92-digit number)

11537430386988987879…98140802328381164159

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