Block #202,119

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 12:43:47 AM · Difficulty 9.8945 · 6,592,022 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

861d5edb4ead0f44a06004fc3257e3ace025abbafd5cceca4d0add9386db3e2d

View on Chainz ↗

Height

#202,119

Difficulty

9.894495

Transactions

Size

5.48 KB

Version

Bits

09e4fd98

Nonce

48,793

Timestamp

10/10/2013, 12:43:47 AM

Confirmations

6,592,022

Merkle Root

559d0b8732843064b47e7dfbb5039328c19f239ac9771eecc8f21b39f99ebe5d

Transactions (2)

Coinbaseb25eaa4ffa951f…5fb6ab5ecbb99f

1 in → 1 out10.2600 XPM110 B

ANvtpRa1…QjsraDJz

4371320d7af404…694c40872f3512

36 in → 2 out3.5137 XPM5.28 KB

AdYDLEKC…CLGKuphh AGckNAHn…PRBRm5T1

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.

2.006 × 10⁹²(93-digit number)

20061002795396432159…65355590048395727339

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

2.006 × 10⁹²(93-digit number)

20061002795396432159…65355590048395727339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.006 × 10⁹²(93-digit number)

20061002795396432159…65355590048395727341

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

4.012 × 10⁹²(93-digit number)

40122005590792864318…30711180096791454679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.012 × 10⁹²(93-digit number)

40122005590792864318…30711180096791454681

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

8.024 × 10⁹²(93-digit number)

80244011181585728637…61422360193582909359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.024 × 10⁹²(93-digit number)

80244011181585728637…61422360193582909361

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

1.604 × 10⁹³(94-digit number)

16048802236317145727…22844720387165818719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10⁹³(94-digit number)

16048802236317145727…22844720387165818721

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

3.209 × 10⁹³(94-digit number)

32097604472634291454…45689440774331637439

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