Block #2,749,177

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/14/2018, 11:03:44 PM · Difficulty 11.6472 · 4,083,407 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

213db71deb347965145bf1456c92d26cc01b788f6a7d7e93510de7f276f22f4b

View on Chainz ↗

Height

#2,749,177

Difficulty

11.647226

Transactions

Size

690 B

Version

Bits

0ba5b09a

Nonce

701,786,634

Timestamp

7/14/2018, 11:03:44 PM

Confirmations

4,083,407

Mined by

⛏️ P2SHAUbHnASDnZU5UsTQjtfAgYjnLKXn8RGoij

Merkle Root

549abb64a609859e8d80ba11bd8b42f92c57a619b70d91c9a5b1003bb0908fcf

Transactions (2)

Coinbase25fb5719704158…a670aab7a8641c

1 in → 1 out7.3700 XPM110 B

AUbHnASD…Xn8RGoij

d1730788dde950…14ede768c000b0

3 in → 2 out10.4100 XPM489 B

AVPbVeZz…KgXmTwBg Aei7Ymdr…MjKXcgCp

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.

5.417 × 10⁹⁷(98-digit number)

54172157111126530858…89581276598505471999

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

5.417 × 10⁹⁷(98-digit number)

54172157111126530858…89581276598505471999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.417 × 10⁹⁷(98-digit number)

54172157111126530858…89581276598505472001

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

1.083 × 10⁹⁸(99-digit number)

10834431422225306171…79162553197010943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.083 × 10⁹⁸(99-digit number)

10834431422225306171…79162553197010944001

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

2.166 × 10⁹⁸(99-digit number)

21668862844450612343…58325106394021887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.166 × 10⁹⁸(99-digit number)

21668862844450612343…58325106394021888001

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

4.333 × 10⁹⁸(99-digit number)

43337725688901224686…16650212788043775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.333 × 10⁹⁸(99-digit number)

43337725688901224686…16650212788043776001

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

8.667 × 10⁹⁸(99-digit number)

86675451377802449373…33300425576087551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.667 × 10⁹⁸(99-digit number)

86675451377802449373…33300425576087552001

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

1.733 × 10⁹⁹(100-digit number)

17335090275560489874…66600851152175103999

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 #2,749,177

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