Block #1,171,340

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/26/2015, 1:32:32 PM · Difficulty 10.9367 · 5,639,812 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ede4d35803364ca1457edf8cdc2807f05eea68940525fe4c479d508fd13286f

View on Chainz ↗

Height

#1,171,340

Difficulty

10.936688

Transactions

Size

3.82 KB

Version

Bits

0aefcac8

Nonce

1,254,790,693

Timestamp

7/26/2015, 1:32:32 PM

Confirmations

5,639,812

Mined by

⛏️ P2SHAGVFYX6W75K39CQNcCqUEyaiqJUcsx8LWQ

Merkle Root

46f9bd52c6f1b45e3bceb49d9fa9c9753771fafd243e3e8624339c548b57f531

Transactions (3)

Coinbase4a52d1e05eacbb…9aa6515e0f516e

1 in → 1 out8.3900 XPM110 B

AGVFYX6W…Ucsx8LWQ

3d00d8be1ed1d7…82bb614d4da23d

6 in → 2 out50.0700 XPM967 B

ANGZk2B9…CKhvim7A AWvND6GC…VJAdnW8k

1d47752ddd0800…3066d5e3e458fd

18 in → 2 out141.2102 XPM2.68 KB

APmPu9oq…yauc8zZg AJVeRHXf…C2yREH1f

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.

1.869 × 10⁹⁴(95-digit number)

18697190066938004603…08172922912858851599

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

1.869 × 10⁹⁴(95-digit number)

18697190066938004603…08172922912858851599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.869 × 10⁹⁴(95-digit number)

18697190066938004603…08172922912858851601

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

3.739 × 10⁹⁴(95-digit number)

37394380133876009206…16345845825717703199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.739 × 10⁹⁴(95-digit number)

37394380133876009206…16345845825717703201

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

7.478 × 10⁹⁴(95-digit number)

74788760267752018412…32691691651435406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.478 × 10⁹⁴(95-digit number)

74788760267752018412…32691691651435406401

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

1.495 × 10⁹⁵(96-digit number)

14957752053550403682…65383383302870812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.495 × 10⁹⁵(96-digit number)

14957752053550403682…65383383302870812801

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

2.991 × 10⁹⁵(96-digit number)

29915504107100807364…30766766605741625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.991 × 10⁹⁵(96-digit number)

29915504107100807364…30766766605741625601

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.983 × 10⁹⁵(96-digit number)

59831008214201614729…61533533211483251199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,171,340

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