Block #2,164,819

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2017, 6:28:40 PM · Difficulty 10.8981 · 4,668,449 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d91757d4f772bfcf5094b14799f5fd0c234f17d21b2eb7c40ad9a1c770db654

View on Chainz ↗

Height

#2,164,819

Difficulty

10.898093

Transactions

Size

3.88 KB

Version

Bits

0ae5e96d

Nonce

157,813,463

Timestamp

6/17/2017, 6:28:40 PM

Confirmations

4,668,449

Mined by

⛏️ P2SHANNWauGKcukwFpPujS5C31GvPEvBZaGWUx

Merkle Root

228b761d2cc166a112b44523926ec821556e2129b7a8d564441cfebc4dba3bcc

Transactions (2)

Coinbasef97023e72d8ff7…6cbcccabd0cf57

1 in → 1 out8.5000 XPM109 B

ANNWauGK…vBZaGWUx

09e20743a20431…76d7b21cc781da

25 in → 2 out0.7628 XPM3.69 KB

AdYAQpPs…RtE6mxjS AJpJB41X…GoMZrzK7

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.

8.823 × 10⁹²(93-digit number)

88234473441060601009…13319793055284551999

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

8.823 × 10⁹²(93-digit number)

88234473441060601009…13319793055284551999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.823 × 10⁹²(93-digit number)

88234473441060601009…13319793055284552001

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

1.764 × 10⁹³(94-digit number)

17646894688212120201…26639586110569103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.764 × 10⁹³(94-digit number)

17646894688212120201…26639586110569104001

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

3.529 × 10⁹³(94-digit number)

35293789376424240403…53279172221138207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.529 × 10⁹³(94-digit number)

35293789376424240403…53279172221138208001

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

7.058 × 10⁹³(94-digit number)

70587578752848480807…06558344442276415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.058 × 10⁹³(94-digit number)

70587578752848480807…06558344442276416001

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

1.411 × 10⁹⁴(95-digit number)

14117515750569696161…13116688884552831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.411 × 10⁹⁴(95-digit number)

14117515750569696161…13116688884552832001

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 #2,164,819

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