Block #1,183,169

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/5/2015, 3:21:38 AM · Difficulty 10.9071 · 5,631,775 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

661579055423831bb49b9d65c3942622da94a0bea069b1c4e1e30c09d3096b32

View on Chainz ↗

Height

#1,183,169

Difficulty

10.907082

Transactions

Size

3.30 KB

Version

Bits

0ae8368e

Nonce

1,397,933,182

Timestamp

8/5/2015, 3:21:38 AM

Confirmations

5,631,775

Mined by

⛏️ P2SHALaPQTmx8o21y4t3sov6C8nVHiFquknv6c

Merkle Root

81ddb87a1b842c4df9104baa406ce5a63961bfc0f4a2440e51d5587b2bcd0022

Transactions (3)

Coinbase8677f1bc8611c5…287a1c48a7ad7f

1 in → 1 out8.4300 XPM110 B

ALaPQTmx…Fquknv6c

152c254add18fb…97b97b4eefea27

2 in → 29 out0.3022 XPM1.26 KB

AXye82rf…8sYSnBud AX6oJXsR…NsFeV4Bn ARG5ac1H…wU4fV4Gv AXLZ1XsT…oQ3J9CRw ATF5aMuD…gKc7Tcff

7a0ed6a14beb81…238f0c3c260cfb

1 in → 51 out2.6953 XPM1.85 KB

AZUp4TdR…bXzb6GME ASfVL6HV…X7TFq6a8 ALexpQLu…S7eUToyX ASj6QvRK…5BqZKge4 AS5G2LFg…rr4LZQzk

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.

2.686 × 10⁹⁵(96-digit number)

26868393059159054366…66239420515630817279

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

2.686 × 10⁹⁵(96-digit number)

26868393059159054366…66239420515630817279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.686 × 10⁹⁵(96-digit number)

26868393059159054366…66239420515630817281

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

5.373 × 10⁹⁵(96-digit number)

53736786118318108732…32478841031261634559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.373 × 10⁹⁵(96-digit number)

53736786118318108732…32478841031261634561

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

1.074 × 10⁹⁶(97-digit number)

10747357223663621746…64957682062523269119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.074 × 10⁹⁶(97-digit number)

10747357223663621746…64957682062523269121

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

2.149 × 10⁹⁶(97-digit number)

21494714447327243492…29915364125046538239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.149 × 10⁹⁶(97-digit number)

21494714447327243492…29915364125046538241

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

4.298 × 10⁹⁶(97-digit number)

42989428894654486985…59830728250093076479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.298 × 10⁹⁶(97-digit number)

42989428894654486985…59830728250093076481

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 #1,183,169

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