Block #411,160

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 1:36:29 PM · Difficulty 10.4308 · 6,406,201 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c37aa7561e8627f74de736f24d983379f670ac2404e2014f83944b33b8162a46

View on Chainz ↗

Height

#411,160

Difficulty

10.430847

Transactions

Size

1.43 KB

Version

Bits

0a6e4c01

Nonce

15,083

Timestamp

2/19/2014, 1:36:29 PM

Confirmations

6,406,201

Mined by

⛏️ FaSDAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d509ce5ecd9ff5666ff495a80bd167cf4c77a16cbbda657474b80333330475fd

Transactions (2)

Coinbase1d2fa7bc8f2454…b91a96343c2704

1 in → 19 out9.1800 XPM709 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

a418129ca1fa90…fd7406b2a1d1dc

4 in → 2 out3.1426 XPM668 B

AeKNrjNj…1NEq95Ta AVkVLBYw…kNh65kqx

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.

1.800 × 10⁹⁸(99-digit number)

18005582064964161431…71544137956053258239

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

1.800 × 10⁹⁸(99-digit number)

18005582064964161431…71544137956053258239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.800 × 10⁹⁸(99-digit number)

18005582064964161431…71544137956053258241

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

3.601 × 10⁹⁸(99-digit number)

36011164129928322862…43088275912106516479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.601 × 10⁹⁸(99-digit number)

36011164129928322862…43088275912106516481

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

7.202 × 10⁹⁸(99-digit number)

72022328259856645724…86176551824213032959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.202 × 10⁹⁸(99-digit number)

72022328259856645724…86176551824213032961

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

1.440 × 10⁹⁹(100-digit number)

14404465651971329144…72353103648426065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.440 × 10⁹⁹(100-digit number)

14404465651971329144…72353103648426065921

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

2.880 × 10⁹⁹(100-digit number)

28808931303942658289…44706207296852131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.880 × 10⁹⁹(100-digit number)

28808931303942658289…44706207296852131841

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 #411,160

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