Block #2,849,506

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/21/2018, 5:17:22 PM · Difficulty 11.7312 · 3,981,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd67c94e2597d049e389d9301c7c2a0331f5b37a878f132e5756fe4c68bcdeab

View on Chainz ↗

Height

#2,849,506

Difficulty

11.731174

Transactions

Size

1.37 KB

Version

Bits

0bbb2e32

Nonce

787,465,141

Timestamp

9/21/2018, 5:17:22 PM

Confirmations

3,981,487

Mined by

⛏️ P2SHAHiMPZaYyQCunjFMRHkuE57yYc9SH9b6WR

Merkle Root

ee39c88058e6814780dda731cf8fbe9f22c06bc0bedf6abb483d22a3157ec5c3

Transactions (5)

Coinbaseb00b4a9b906b6b…03dc051ccf67a1

1 in → 1 out7.2900 XPM110 B

AHiMPZaY…9SH9b6WR

a0b21b33da7f4b…8853753c9873d0

1 in → 2 out6.7238 XPM226 B

AevxZoN3…fwTLU9Fn AanuqxCr…ou1HCRoH

b366aa557ae942…257f1a6092bb1e

2 in → 2 out6.4666 XPM373 B

AXSDamw3…ZLdH1Ufx AbHT5sE7…7TPSneVy

0ff0c68351dcfc…1ccd88d7520bd5

1 in → 2 out3.2340 XPM226 B

AUKAcxSf…oYoxGhbp ANjTQp24…sVkz8Xup

4fab746c34b8c2…322c07820721db

2 in → 2 out0.5139 XPM373 B

AQc7pF1d…i9EGGKqy Aatwb5m5…CpUGXNMa

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.

1.421 × 10⁹⁸(99-digit number)

14211474041503133586…85767039354809221119

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

1.421 × 10⁹⁸(99-digit number)

14211474041503133586…85767039354809221119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.421 × 10⁹⁸(99-digit number)

14211474041503133586…85767039354809221121

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

2.842 × 10⁹⁸(99-digit number)

28422948083006267172…71534078709618442239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.842 × 10⁹⁸(99-digit number)

28422948083006267172…71534078709618442241

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

5.684 × 10⁹⁸(99-digit number)

56845896166012534344…43068157419236884479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.684 × 10⁹⁸(99-digit number)

56845896166012534344…43068157419236884481

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

1.136 × 10⁹⁹(100-digit number)

11369179233202506868…86136314838473768959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.136 × 10⁹⁹(100-digit number)

11369179233202506868…86136314838473768961

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

2.273 × 10⁹⁹(100-digit number)

22738358466405013737…72272629676947537919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.273 × 10⁹⁹(100-digit number)

22738358466405013737…72272629676947537921

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

4.547 × 10⁹⁹(100-digit number)

45476716932810027475…44545259353895075839

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 #2,849,506

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