Block #189,206

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 4:16:36 PM · Difficulty 9.8725 · 6,600,627 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27fc218c71da751eb2dee59898bad264c89096632cf4e1054d7219a25f0ba3bc

View on Chainz ↗

Height

#189,206

Difficulty

9.872468

Transactions

Size

198 B

Version

Bits

09df5a11

Nonce

69,279

Timestamp

10/1/2013, 4:16:36 PM

Confirmations

6,600,627

Merkle Root

72c82c7b2720eaf5aaf141690a3e539b8988546e0a5bb348d3a1d1567ef00dce

Transactions (1)

Coinbase72c82c7b2720ea…a1d1567ef00dce

1 in → 1 out10.2400 XPM109 B

AZv7gMUK…CbiASjGW

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.

2.498 × 10⁹³(94-digit number)

24981332128456055684…09643212811926812859

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

2.498 × 10⁹³(94-digit number)

24981332128456055684…09643212811926812859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.498 × 10⁹³(94-digit number)

24981332128456055684…09643212811926812861

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

4.996 × 10⁹³(94-digit number)

49962664256912111369…19286425623853625719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.996 × 10⁹³(94-digit number)

49962664256912111369…19286425623853625721

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

9.992 × 10⁹³(94-digit number)

99925328513824222738…38572851247707251439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.992 × 10⁹³(94-digit number)

99925328513824222738…38572851247707251441

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

1.998 × 10⁹⁴(95-digit number)

19985065702764844547…77145702495414502879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.998 × 10⁹⁴(95-digit number)

19985065702764844547…77145702495414502881

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

3.997 × 10⁹⁴(95-digit number)

39970131405529689095…54291404990829005759

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