Block #2,175,260

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/24/2017, 9:51:55 AM · Difficulty 10.9147 · 4,668,534 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

775fcf0413507816c0720e834b3cd0f4e39a46913285903e97df527026b898f2

View on Chainz ↗

Height

#2,175,260

Difficulty

10.914667

Transactions

Size

1.73 KB

Version

Bits

0aea279c

Nonce

938,845,634

Timestamp

6/24/2017, 9:51:55 AM

Confirmations

4,668,534

Mined by

⛏️ P2SHAUWFEpcxAMcSUS7No3RPYBcTJbdsH8tpFN

Merkle Root

449585d96f3a2a3983d3bd08894e8a94d084fc0abb78b5e0c79bd16661b4497e

Transactions (4)

Coinbasecc1f1abcf12081…fe258a136de419

1 in → 1 out8.4200 XPM110 B

AUWFEpcx…dsH8tpFN

309f3b509f45d7…8f0e536af5546a

1 in → 2 out2032.3854 XPM225 B

AXNhQkvH…hHH6G1qY Ad1keczS…bFWLLmjM

f67c51f1e50c1a…9d2795bf75ccb4

1 in → 2 out4.1749 XPM227 B

Af5CjUvP…DwjhdfTy AeYZTP6b…v53Q54vJ

0d6a2feb2f75ed…e528afe9cd36a3

7 in → 2 out5.0409 XPM1.09 KB

AN4s4bb4…8sL1AkRU ARhcVK7d…inpLNQpo

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.

1.744 × 10⁹⁶(97-digit number)

17442417219582427855…75950083535017492479

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

1.744 × 10⁹⁶(97-digit number)

17442417219582427855…75950083535017492479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.744 × 10⁹⁶(97-digit number)

17442417219582427855…75950083535017492481

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

3.488 × 10⁹⁶(97-digit number)

34884834439164855711…51900167070034984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.488 × 10⁹⁶(97-digit number)

34884834439164855711…51900167070034984961

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

6.976 × 10⁹⁶(97-digit number)

69769668878329711423…03800334140069969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.976 × 10⁹⁶(97-digit number)

69769668878329711423…03800334140069969921

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

1.395 × 10⁹⁷(98-digit number)

13953933775665942284…07600668280139939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.395 × 10⁹⁷(98-digit number)

13953933775665942284…07600668280139939841

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

2.790 × 10⁹⁷(98-digit number)

27907867551331884569…15201336560279879679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.790 × 10⁹⁷(98-digit number)

27907867551331884569…15201336560279879681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,175,260

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