Block #2,165,048

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2017, 10:22:33 PM · Difficulty 10.8980 · 4,678,207 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9a0b6f59fce9122d128d7ce5a5554e608714accf15a571be52729694c669c6c

View on Chainz ↗

Height

#2,165,048

Difficulty

10.897987

Transactions

Size

1.38 KB

Version

Bits

0ae5e27b

Nonce

1,812,005,758

Timestamp

6/17/2017, 10:22:33 PM

Confirmations

4,678,207

Mined by

⛏️ P2SHALCDj5T8DVsTZXDtRdzQm2QKKtcTHuDE3k

Merkle Root

ce974d4ac69902c0709899bb167ef45e79265d1c3b41e6dfacdeb244b1141871

Transactions (5)

Coinbase3ed416cb3ca9aa…8d0501ca7c8ad8

1 in → 1 out8.4500 XPM110 B

ALCDj5T8…cTHuDE3k

efa4e152d6ecb3…476ff8ad6b52b0

3 in → 2 out4915.5390 XPM523 B

AFu8Uki1…56FXRCu7 AZAUpPRK…y6qkZdaT

d9de9f95399a7d…559aeb07a569a3

2 in → 2 out16.8100 XPM307 B

AJ2RuwMk…pKAsxakN ARezZb4y…FxP7ivbi

9f4ccb3efb415b…b33507ef142731

1 in → 2 out8.3900 XPM192 B

AQipFUJn…CdwxNcQS ASyjxXAn…eR9MH6i9

a38acf858a1cde…c3ccb89fbb8b92

1 in → 2 out8.3900 XPM193 B

AbRiioqF…KorQ2YQW AbKdU8pk…mnpWmLzt

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.

4.123 × 10⁹⁴(95-digit number)

41232523807513914032…76111842420075928639

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

4.123 × 10⁹⁴(95-digit number)

41232523807513914032…76111842420075928639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.123 × 10⁹⁴(95-digit number)

41232523807513914032…76111842420075928641

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

8.246 × 10⁹⁴(95-digit number)

82465047615027828065…52223684840151857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.246 × 10⁹⁴(95-digit number)

82465047615027828065…52223684840151857281

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

1.649 × 10⁹⁵(96-digit number)

16493009523005565613…04447369680303714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.649 × 10⁹⁵(96-digit number)

16493009523005565613…04447369680303714561

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

3.298 × 10⁹⁵(96-digit number)

32986019046011131226…08894739360607429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.298 × 10⁹⁵(96-digit number)

32986019046011131226…08894739360607429121

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

6.597 × 10⁹⁵(96-digit number)

65972038092022262452…17789478721214858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.597 × 10⁹⁵(96-digit number)

65972038092022262452…17789478721214858241

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 #2,165,048

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