Block #2,845,756

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/19/2018, 3:13:37 AM · Difficulty 11.7298 · 3,996,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10d83a2fbb7a9414fbf1259e82ec05283897e678ceb87b6e01c55c03b328d202

View on Chainz ↗

Height

#2,845,756

Difficulty

11.729765

Transactions

Size

1.66 KB

Version

Bits

0bbad1e1

Nonce

419,540,842

Timestamp

9/19/2018, 3:13:37 AM

Confirmations

3,996,365

Mined by

⛏️ P2SHAPRGdmEAQustbkA7HbHgzf3Q9paw7E4x5c

Merkle Root

9855963da8ee95072cd33d0edc55bbe69cf9d3fe96b3097e3373d859c05386cb

Transactions (5)

Coinbase48922581566106…910194a1986e09

1 in → 1 out7.3000 XPM110 B

APRGdmEA…aw7E4x5c

d54916b2b99f43…61c2243a96c6c9

2 in → 2 out4.0887 XPM374 B

AVuDDxxK…NJMBNHSh AWLhispt…YegP97ro

3a2ea977d585f4…1dc93d8eef83c6

1 in → 2 out1.2037 XPM225 B

AGbm9W17…Jvw6eg2t AWcKCLGL…DzXr4LWA

bf3e78d79c6ed5…6631d84d2bebc4

1 in → 2 out1.7357 XPM226 B

AWvUqpmT…5kxY2JWz AepyHUmx…QYcCRqK4

517e1209223bb3…dbdd83d519485d

4 in → 2 out2.0150 XPM671 B

AazEN1Eq…rhXGiemo ANfF3SCe…5eCA5XFx

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.

1.481 × 10⁹⁶(97-digit number)

14818010931251137258…51690407521042477439

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

1.481 × 10⁹⁶(97-digit number)

14818010931251137258…51690407521042477439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.481 × 10⁹⁶(97-digit number)

14818010931251137258…51690407521042477441

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

2.963 × 10⁹⁶(97-digit number)

29636021862502274517…03380815042084954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.963 × 10⁹⁶(97-digit number)

29636021862502274517…03380815042084954881

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

5.927 × 10⁹⁶(97-digit number)

59272043725004549035…06761630084169909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.927 × 10⁹⁶(97-digit number)

59272043725004549035…06761630084169909761

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

1.185 × 10⁹⁷(98-digit number)

11854408745000909807…13523260168339819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.185 × 10⁹⁷(98-digit number)

11854408745000909807…13523260168339819521

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

2.370 × 10⁹⁷(98-digit number)

23708817490001819614…27046520336679639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.370 × 10⁹⁷(98-digit number)

23708817490001819614…27046520336679639041

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

4.741 × 10⁹⁷(98-digit number)

47417634980003639228…54093040673359278079

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 #2,845,756

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