Block #2,834,464

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/11/2018, 11:28:16 AM · Difficulty 11.7146 · 3,997,274 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a556c29a5da384459f60c45ecb87543b83a0e16bc2415f775f666a77112aeac2

View on Chainz ↗

Height

#2,834,464

Difficulty

11.714602

Transactions

Size

959 B

Version

Bits

0bb6f025

Nonce

630,970,576

Timestamp

9/11/2018, 11:28:16 AM

Confirmations

3,997,274

Mined by

⛏️ P2SHAeAi1dUsiBFhEr3UTbyGHNMrWdbXRai9hg

Merkle Root

d96f761cf4973e72dc3ab5a9e374571a368485b8a8e0c92b379096bd76186914

Transactions (4)

Coinbase2e1373f0569df7…9709b32b639011

1 in → 1 out7.3000 XPM110 B

AeAi1dUs…bXRai9hg

6417e3bd350032…ca8065d3238e9e

1 in → 2 out7.2600 XPM191 B

AXwoWUz6…287PGZc9 AYUY6QBZ…nstBEWCQ

c13319dac76496…e59460a96c2167

1 in → 2 out7.2600 XPM193 B

AcLX2XaT…QZybuX8C APYhGooL…tTACMvay

6ae84a38bd43f2…6748347f12dea8

2 in → 2 out4.0508 XPM375 B

AWaYC9BA…1BzTFe5J AWEUmuSL…2WWEN9nS

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.

5.283 × 10⁹³(94-digit number)

52835199845204075745…80723301580506303579

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

5.283 × 10⁹³(94-digit number)

52835199845204075745…80723301580506303579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.283 × 10⁹³(94-digit number)

52835199845204075745…80723301580506303581

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

1.056 × 10⁹⁴(95-digit number)

10567039969040815149…61446603161012607159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.056 × 10⁹⁴(95-digit number)

10567039969040815149…61446603161012607161

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

2.113 × 10⁹⁴(95-digit number)

21134079938081630298…22893206322025214319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.113 × 10⁹⁴(95-digit number)

21134079938081630298…22893206322025214321

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

4.226 × 10⁹⁴(95-digit number)

42268159876163260596…45786412644050428639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.226 × 10⁹⁴(95-digit number)

42268159876163260596…45786412644050428641

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

8.453 × 10⁹⁴(95-digit number)

84536319752326521192…91572825288100857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.453 × 10⁹⁴(95-digit number)

84536319752326521192…91572825288100857281

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

1.690 × 10⁹⁵(96-digit number)

16907263950465304238…83145650576201714559

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 #2,834,464

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