Block #2,168,743

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/20/2017, 11:39:32 AM · Difficulty 10.8985 · 4,657,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dc226d0e26f10e3a98a2a472abf02d6ee20195f860932adf10879ce52813392

View on Chainz ↗

Height

#2,168,743

Difficulty

10.898471

Transactions

Size

2.15 KB

Version

Bits

0ae60236

Nonce

2,125,135,242

Timestamp

6/20/2017, 11:39:32 AM

Confirmations

4,657,930

Mined by

⛏️ P2SHAY1iAx4YhdbYhrLARy82BQVjdqzcSpJJjk

Merkle Root

ffaa31a50295f90425ffcae2e07c470a7fb730b38130a020c27cba89827ae808

Transactions (2)

Coinbasea09ffec42b5187…cf3fc5be39085e

1 in → 1 out8.5500 XPM109 B

AY1iAx4Y…zcSpJJjk

bd6fda24bd70ad…eb3410dcf0bb6c

13 in → 2 out455.7038 XPM1.95 KB

AVB8Kqgj…zUanL8Tf Ab2K3G76…ZYx3xuVm

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.

4.982 × 10⁹⁶(97-digit number)

49821133283434478661…64997775307821875199

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

4.982 × 10⁹⁶(97-digit number)

49821133283434478661…64997775307821875199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.982 × 10⁹⁶(97-digit number)

49821133283434478661…64997775307821875201

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

9.964 × 10⁹⁶(97-digit number)

99642266566868957323…29995550615643750399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.964 × 10⁹⁶(97-digit number)

99642266566868957323…29995550615643750401

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

1.992 × 10⁹⁷(98-digit number)

19928453313373791464…59991101231287500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.992 × 10⁹⁷(98-digit number)

19928453313373791464…59991101231287500801

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

3.985 × 10⁹⁷(98-digit number)

39856906626747582929…19982202462575001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.985 × 10⁹⁷(98-digit number)

39856906626747582929…19982202462575001601

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

7.971 × 10⁹⁷(98-digit number)

79713813253495165858…39964404925150003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.971 × 10⁹⁷(98-digit number)

79713813253495165858…39964404925150003201

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 #2,168,743

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