Block #2,910,413

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/4/2018, 11:17:07 PM · Difficulty 11.5332 · 3,923,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48b3c614f962cc63f4d937e7bd78432910c881b829870edb055145455ce7d6bf

View on Chainz ↗

Height

#2,910,413

Difficulty

11.533231

Transactions

Size

1.14 KB

Version

Bits

0b8881d9

Nonce

380,075,354

Timestamp

11/4/2018, 11:17:07 PM

Confirmations

3,923,511

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

fa3a809263d47798bc485e8fc7a6a147da522501eef1997b29615865e37e11ab

Transactions (2)

Coinbase0cdf0b5d8b1d50…2d06b9bd49fa2f

1 in → 1 out7.5500 XPM110 B

AUMQRepm…tAfKmdW1

b80237ab4e8969…8fd01549ff6797

6 in → 2 out1326.6491 XPM963 B

ANAYeyDi…P2URm1oP AQPqLzdY…myJxojpr

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.

4.936 × 10⁹⁵(96-digit number)

49368116070284632205…95007341027174801639

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

4.936 × 10⁹⁵(96-digit number)

49368116070284632205…95007341027174801639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.936 × 10⁹⁵(96-digit number)

49368116070284632205…95007341027174801641

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

9.873 × 10⁹⁵(96-digit number)

98736232140569264411…90014682054349603279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.873 × 10⁹⁵(96-digit number)

98736232140569264411…90014682054349603281

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

1.974 × 10⁹⁶(97-digit number)

19747246428113852882…80029364108699206559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.974 × 10⁹⁶(97-digit number)

19747246428113852882…80029364108699206561

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

3.949 × 10⁹⁶(97-digit number)

39494492856227705764…60058728217398413119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.949 × 10⁹⁶(97-digit number)

39494492856227705764…60058728217398413121

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

7.898 × 10⁹⁶(97-digit number)

78988985712455411529…20117456434796826239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.898 × 10⁹⁶(97-digit number)

78988985712455411529…20117456434796826241

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

1.579 × 10⁹⁷(98-digit number)

15797797142491082305…40234912869593652479

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 #2,910,413

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