Block #2,915,478

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/9/2018, 1:28:26 AM · Difficulty 11.4504 · 3,927,340 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d345101f2a10c890099e5994ff54b06cfa17f36293e32fea4fc1b2b191ecef53

View on Chainz ↗

Height

#2,915,478

Difficulty

11.450355

Transactions

Size

1.11 KB

Version

Bits

0b734a6f

Nonce

873,613,456

Timestamp

11/9/2018, 1:28:26 AM

Confirmations

3,927,340

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

67aa3d18eb1c39ac226f12608ab46080c01a45670f51164513a3d2143253dc8e

Transactions (4)

Coinbase65100439fb27a7…b0afa0ae171ae6

1 in → 1 out7.6400 XPM109 B

AbXwmGxD…4XXYP765

4a671553d5d291…bf81b52e7c2e0c

2 in → 2 out10.8624 XPM340 B

AbXwmGxD…4XXYP765 ARKFud7A…JRaX29qB

b27d4efb7e430e…550dcd791788b5

2 in → 2 out4.9000 XPM374 B

AMLiyYLv…iYQLf2JU AUhjokok…k5m93PZR

0cec1e212f7e11…76d885648358b8

1 in → 2 out5.4754 XPM225 B

AevxZoN3…fwTLU9Fn AbXwmGxD…4XXYP765

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.

1.725 × 10⁹³(94-digit number)

17254457903368652523…26702769650615001599

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

1.725 × 10⁹³(94-digit number)

17254457903368652523…26702769650615001599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.725 × 10⁹³(94-digit number)

17254457903368652523…26702769650615001601

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

3.450 × 10⁹³(94-digit number)

34508915806737305047…53405539301230003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.450 × 10⁹³(94-digit number)

34508915806737305047…53405539301230003201

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

6.901 × 10⁹³(94-digit number)

69017831613474610095…06811078602460006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.901 × 10⁹³(94-digit number)

69017831613474610095…06811078602460006401

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

1.380 × 10⁹⁴(95-digit number)

13803566322694922019…13622157204920012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.380 × 10⁹⁴(95-digit number)

13803566322694922019…13622157204920012801

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

2.760 × 10⁹⁴(95-digit number)

27607132645389844038…27244314409840025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.760 × 10⁹⁴(95-digit number)

27607132645389844038…27244314409840025601

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

5.521 × 10⁹⁴(95-digit number)

55214265290779688076…54488628819680051199

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 #2,915,478

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