Block #2,163,117

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2017, 11:55:29 AM · Difficulty 10.9007 · 4,668,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ef32f4a1592b086ea3526002e36b3b542a05d69b69cd1d150f09785a098d7b7

View on Chainz ↗

Height

#2,163,117

Difficulty

10.900680

Transactions

Size

3.89 KB

Version

Bits

0ae692f1

Nonce

320,130,605

Timestamp

6/16/2017, 11:55:29 AM

Confirmations

4,668,488

Mined by

⛏️ P2SHAMNxtyEfaSji93NUnansmmzHUJHRmDcTjj

Merkle Root

40ed092f962e8f148bfed5edd6d1d48a0b6d6a0f3cb7c610faa33fd3c36429aa

Transactions (3)

Coinbase4b101bd897c9cc…fca22251418193

1 in → 1 out8.4800 XPM110 B

AMNxtyEf…HRmDcTjj

bf14a641d25ae9…50148b75341a74

9 in → 1 out422.7937 XPM1.34 KB

AGxk1TD6…rMWoF8Ha

4521e85ed94fe6…20fe7a6628fa23

16 in → 1 out442.3240 XPM2.36 KB

AdXSigFn…Xt9FMnbf

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.

4.111 × 10⁹⁵(96-digit number)

41119310955346624134…91459253035686461439

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

4.111 × 10⁹⁵(96-digit number)

41119310955346624134…91459253035686461439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.111 × 10⁹⁵(96-digit number)

41119310955346624134…91459253035686461441

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

8.223 × 10⁹⁵(96-digit number)

82238621910693248269…82918506071372922879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.223 × 10⁹⁵(96-digit number)

82238621910693248269…82918506071372922881

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

1.644 × 10⁹⁶(97-digit number)

16447724382138649653…65837012142745845759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.644 × 10⁹⁶(97-digit number)

16447724382138649653…65837012142745845761

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

3.289 × 10⁹⁶(97-digit number)

32895448764277299307…31674024285491691519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.289 × 10⁹⁶(97-digit number)

32895448764277299307…31674024285491691521

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

6.579 × 10⁹⁶(97-digit number)

65790897528554598615…63348048570983383039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.579 × 10⁹⁶(97-digit number)

65790897528554598615…63348048570983383041

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 #2,163,117

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