Block #2,177,591

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 3:58:37 PM · Difficulty 10.9232 · 4,659,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c27df2f3886053022e9ce2584c395deaa395a10bd0875adf5835141fdb9e83f1

View on Chainz ↗

Height

#2,177,591

Difficulty

10.923168

Transactions

Size

876 B

Version

Bits

0aec54b7

Nonce

1,685,310,688

Timestamp

6/25/2017, 3:58:37 PM

Confirmations

4,659,329

Mined by

⛏️ P2SHALCX7AwNCW9gd3drnoq4R66XL5vkRAtpE7

Merkle Root

26b62f7afa6f8cd4429e3abe8f514a8f00b3b7997dfca0ff9297fdc2e58aa6a3

Transactions (4)

Coinbased522d7b9f98408…0553ec693e21fa

1 in → 1 out8.4000 XPM109 B

ALCX7AwN…vkRAtpE7

c411231b0a8204…7633162a992541

1 in → 2 out8070.7468 XPM226 B

AammHJuN…yaRcHuV7 AQNk77NE…P8wAZMpH

0ee3e1cf24bb7a…408aa4a0f94869

1 in → 2 out6046.8517 XPM225 B

ASnwrEPZ…Wy7o9hdc AammHJuN…yaRcHuV7

d41339dcb89f6c…41f775ad7807ec

1 in → 2 out708.0988 XPM227 B

AN8szP8k…CGjYtVjh ARJaNi5X…DkCcGLAZ

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.

3.335 × 10⁹³(94-digit number)

33354330558393456987…95355181015057096959

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

3.335 × 10⁹³(94-digit number)

33354330558393456987…95355181015057096959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.335 × 10⁹³(94-digit number)

33354330558393456987…95355181015057096961

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

6.670 × 10⁹³(94-digit number)

66708661116786913974…90710362030114193919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.670 × 10⁹³(94-digit number)

66708661116786913974…90710362030114193921

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

1.334 × 10⁹⁴(95-digit number)

13341732223357382794…81420724060228387839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.334 × 10⁹⁴(95-digit number)

13341732223357382794…81420724060228387841

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

2.668 × 10⁹⁴(95-digit number)

26683464446714765589…62841448120456775679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.668 × 10⁹⁴(95-digit number)

26683464446714765589…62841448120456775681

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

5.336 × 10⁹⁴(95-digit number)

53366928893429531179…25682896240913551359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.336 × 10⁹⁴(95-digit number)

53366928893429531179…25682896240913551361

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 #2,177,591

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