Block #2,923,711

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/15/2018, 7:27:02 AM · Difficulty 11.3607 · 3,919,380 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af30afa2f1fa4bd18627a4567350b61449b95f3937dacacf29dd36bfbacfcba1

View on Chainz ↗

Height

#2,923,711

Difficulty

11.360651

Transactions

Size

1017 B

Version

Bits

0b5c53a3

Nonce

159,692,831

Timestamp

11/15/2018, 7:27:02 AM

Confirmations

3,919,380

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

741d65f87bd75cbf3669a5c712524f2f6c9a81f17ce520088ac357e3d44bde05

Transactions (2)

Coinbase10a4c005b20c0c…271b22c2524f51

1 in → 1 out7.7500 XPM109 B

AUMQRepm…tAfKmdW1

84a64a0ed1eb82…c27be54b6629f0

5 in → 2 out559.2109 XPM818 B

ALd65iyx…WC2oooUw ALGCmMmW…PqMriFY3

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.

9.715 × 10⁹⁴(95-digit number)

97159654644908326823…56670913189752382399

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

9.715 × 10⁹⁴(95-digit number)

97159654644908326823…56670913189752382399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.715 × 10⁹⁴(95-digit number)

97159654644908326823…56670913189752382401

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

1.943 × 10⁹⁵(96-digit number)

19431930928981665364…13341826379504764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.943 × 10⁹⁵(96-digit number)

19431930928981665364…13341826379504764801

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

3.886 × 10⁹⁵(96-digit number)

38863861857963330729…26683652759009529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.886 × 10⁹⁵(96-digit number)

38863861857963330729…26683652759009529601

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

7.772 × 10⁹⁵(96-digit number)

77727723715926661458…53367305518019059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.772 × 10⁹⁵(96-digit number)

77727723715926661458…53367305518019059201

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

1.554 × 10⁹⁶(97-digit number)

15545544743185332291…06734611036038118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.554 × 10⁹⁶(97-digit number)

15545544743185332291…06734611036038118401

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

3.109 × 10⁹⁶(97-digit number)

31091089486370664583…13469222072076236799

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 #2,923,711

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