Block #2,165,888

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2017, 12:10:21 PM · Difficulty 10.8983 · 4,659,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24b721660475011e8fb9aeb5db57cac4320d0dee9a0a88837e022c33a9c417ec

View on Chainz ↗

Height

#2,165,888

Difficulty

10.898292

Transactions

Size

4.21 KB

Version

Bits

0ae5f679

Nonce

1,213,345,967

Timestamp

6/18/2017, 12:10:21 PM

Confirmations

4,659,771

Mined by

⛏️ P2SHAf5bhedwg1vaNv7VbDc2Vh3HBpaDvteyJP

Merkle Root

18fee46f6f11bfa51a55d75efbe5db9cc3b2f0a6789f8064e17d25a01b3a3d0a

Transactions (2)

Coinbase342aba5e984303…58797bbe3b2b9c

1 in → 1 out8.4600 XPM109 B

Af5bhedw…aDvteyJP

c6d2c7e9f5398a…61aa06d81d2d2e

27 in → 3 out3120.0122 XPM4.01 KB

AURERLoH…qfihJDAY AbSihS6q…PPdLXDv8 Ac7abfJW…KmkwQerd

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.

2.021 × 10⁹⁶(97-digit number)

20212138181051429041…94674988563304092159

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

2.021 × 10⁹⁶(97-digit number)

20212138181051429041…94674988563304092159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.021 × 10⁹⁶(97-digit number)

20212138181051429041…94674988563304092161

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

4.042 × 10⁹⁶(97-digit number)

40424276362102858082…89349977126608184319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.042 × 10⁹⁶(97-digit number)

40424276362102858082…89349977126608184321

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

8.084 × 10⁹⁶(97-digit number)

80848552724205716164…78699954253216368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.084 × 10⁹⁶(97-digit number)

80848552724205716164…78699954253216368641

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

1.616 × 10⁹⁷(98-digit number)

16169710544841143232…57399908506432737279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.616 × 10⁹⁷(98-digit number)

16169710544841143232…57399908506432737281

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

3.233 × 10⁹⁷(98-digit number)

32339421089682286465…14799817012865474559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.233 × 10⁹⁷(98-digit number)

32339421089682286465…14799817012865474561

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 #2,165,888

Cookie Preferences