Block #2,913,465

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/7/2018, 8:44:17 AM · Difficulty 11.4953 · 3,927,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b374132ef36f3538c56fba533d7bb2d988bf62279af29e4381935cc70413f593

View on Chainz ↗

Height

#2,913,465

Difficulty

11.495284

Transactions

Size

2.12 KB

Version

Bits

0b7ecae8

Nonce

1,731,335,123

Timestamp

11/7/2018, 8:44:17 AM

Confirmations

3,927,224

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

976aa92a0dbb46273c1aa021ec39b0d74b6e6393fa33ed04b84e9f12ff55653c

Transactions (2)

Coinbase6c3c08d30edef8…d345c54cf88cb9

1 in → 1 out7.5800 XPM110 B

AbXwmGxD…4XXYP765

80b006bbd9a107…bcaad56d33db98

13 in → 1 out110.0000 XPM1.92 KB

ANtZtAHH…hWzfwEBq

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.

3.929 × 10⁹⁵(96-digit number)

39299133418111449678…21179758634755238399

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

3.929 × 10⁹⁵(96-digit number)

39299133418111449678…21179758634755238399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.929 × 10⁹⁵(96-digit number)

39299133418111449678…21179758634755238401

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

7.859 × 10⁹⁵(96-digit number)

78598266836222899357…42359517269510476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.859 × 10⁹⁵(96-digit number)

78598266836222899357…42359517269510476801

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

1.571 × 10⁹⁶(97-digit number)

15719653367244579871…84719034539020953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.571 × 10⁹⁶(97-digit number)

15719653367244579871…84719034539020953601

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

3.143 × 10⁹⁶(97-digit number)

31439306734489159743…69438069078041907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.143 × 10⁹⁶(97-digit number)

31439306734489159743…69438069078041907201

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

6.287 × 10⁹⁶(97-digit number)

62878613468978319486…38876138156083814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.287 × 10⁹⁶(97-digit number)

62878613468978319486…38876138156083814401

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

1.257 × 10⁹⁷(98-digit number)

12575722693795663897…77752276312167628799

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 #2,913,465

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