Block #2,320,882

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/3/2017, 2:00:15 PM · Difficulty 10.9203 · 4,520,948 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2bf6348e5a9f98c3fb0468862cd9fb4b3b7b40cd9fe650687bedc67d7c4acf8

View on Chainz ↗

Height

#2,320,882

Difficulty

10.920327

Transactions

Size

1.79 KB

Version

Bits

0aeb9a93

Nonce

1,073,029,078

Timestamp

10/3/2017, 2:00:15 PM

Confirmations

4,520,948

Mined by

⛏️ P2SHAWWBJxwyGxTMTyrqGnTjNiTkBkbAwM3Dp2

Merkle Root

efee204e92a5db594407c9c4cf16ffddaf13dc17ec589b3c19512022703e064d

Transactions (3)

Coinbasee08d6d17d497cd…27393221b14f84

1 in → 1 out8.4000 XPM109 B

AWWBJxwy…bAwM3Dp2

4ce8af5aa206f0…aae32d88eb7afb

9 in → 2 out1309.2778 XPM1.38 KB

AZctvh2i…k1EpNrgB AbfHPQRP…cc1QCTYa

a9bc85bc175b7b…daf3cb41e95ea4

1 in → 2 out41750.1817 XPM225 B

ANdsz5uE…NDhTWwEi AZ3MJJ7f…HYK2pcC8

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.

1.780 × 10⁹⁴(95-digit number)

17808947410552656353…86173799470421957119

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

1.780 × 10⁹⁴(95-digit number)

17808947410552656353…86173799470421957119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.780 × 10⁹⁴(95-digit number)

17808947410552656353…86173799470421957121

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

3.561 × 10⁹⁴(95-digit number)

35617894821105312706…72347598940843914239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.561 × 10⁹⁴(95-digit number)

35617894821105312706…72347598940843914241

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

7.123 × 10⁹⁴(95-digit number)

71235789642210625413…44695197881687828479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.123 × 10⁹⁴(95-digit number)

71235789642210625413…44695197881687828481

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

1.424 × 10⁹⁵(96-digit number)

14247157928442125082…89390395763375656959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.424 × 10⁹⁵(96-digit number)

14247157928442125082…89390395763375656961

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

2.849 × 10⁹⁵(96-digit number)

28494315856884250165…78780791526751313919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.849 × 10⁹⁵(96-digit number)

28494315856884250165…78780791526751313921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.698 × 10⁹⁵(96-digit number)

56988631713768500331…57561583053502627839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,320,882

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