Block #2,176,016

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/24/2017, 7:19:06 PM · Difficulty 10.9178 · 4,651,216 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26c273a908cc0c196a79813fbc75d9b3b52f494bd9abffd6d282de95326c8bf8

View on Chainz ↗

Height

#2,176,016

Difficulty

10.917828

Transactions

Size

1.72 KB

Version

Bits

0aeaf6c3

Nonce

51,206,823

Timestamp

6/24/2017, 7:19:06 PM

Confirmations

4,651,216

Mined by

⛏️ P2SHAK3SAZLTXwwfoCdoutsDavaqSAVGnPLWFC

Merkle Root

9fcddb1c9101dfe58584b91b65f246b6533a5f97469bf4faeadc27fe49de84e3

Transactions (2)

Coinbase022bb0a9095b5e…e4c1c96e61b932

1 in → 1 out8.4000 XPM110 B

AK3SAZLT…VGnPLWFC

12e9d406e049ec…132170d6d5fc7a

10 in → 2 out5.8839 XPM1.52 KB

AHB3yTNR…rLC4BFZ3 Ae2fZRJU…UgBKb6g6

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.

5.254 × 10⁹⁷(98-digit number)

52547866498858120031…76252865441559429119

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

5.254 × 10⁹⁷(98-digit number)

52547866498858120031…76252865441559429119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.254 × 10⁹⁷(98-digit number)

52547866498858120031…76252865441559429121

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

1.050 × 10⁹⁸(99-digit number)

10509573299771624006…52505730883118858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.050 × 10⁹⁸(99-digit number)

10509573299771624006…52505730883118858241

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

2.101 × 10⁹⁸(99-digit number)

21019146599543248012…05011461766237716479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.101 × 10⁹⁸(99-digit number)

21019146599543248012…05011461766237716481

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

4.203 × 10⁹⁸(99-digit number)

42038293199086496025…10022923532475432959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.203 × 10⁹⁸(99-digit number)

42038293199086496025…10022923532475432961

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

8.407 × 10⁹⁸(99-digit number)

84076586398172992050…20045847064950865919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.407 × 10⁹⁸(99-digit number)

84076586398172992050…20045847064950865921

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

1.681 × 10⁹⁹(100-digit number)

16815317279634598410…40091694129901731839

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 #2,176,016

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