Block #1,158,790

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/17/2015, 12:21:33 PM · Difficulty 10.9421 · 5,683,999 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33e9f9525f4f2cd2ee2f66d96f47d9871f5223fbb2cdec5ce7e4bf4cb03aa35c

View on Chainz ↗

Height

#1,158,790

Difficulty

10.942094

Transactions

Size

722 B

Version

Bits

0af12d12

Nonce

549,117,876

Timestamp

7/17/2015, 12:21:33 PM

Confirmations

5,683,999

Mined by

⛏️ P2SHAddzcKKoPpa7x34oYNgkdMjgKBXJy6pPMR

Merkle Root

b487dd27c8460327483eb37cd3a427362d77808dee88406c743811fcee038890

Transactions (2)

Coinbase235fbaf7dc557a…130dfb47eef25b

1 in → 1 out8.3500 XPM110 B

AddzcKKo…XJy6pPMR

d245dba2b269c9…c12573627e18c3

3 in → 2 out447.9755 XPM520 B

AeVFaBao…VrxTMC9j AaE7NnjM…tcui5of2

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.

4.848 × 10⁹⁸(99-digit number)

48480962140413100208…18841446142983208959

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

4.848 × 10⁹⁸(99-digit number)

48480962140413100208…18841446142983208959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.848 × 10⁹⁸(99-digit number)

48480962140413100208…18841446142983208961

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

9.696 × 10⁹⁸(99-digit number)

96961924280826200416…37682892285966417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.696 × 10⁹⁸(99-digit number)

96961924280826200416…37682892285966417921

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

1.939 × 10⁹⁹(100-digit number)

19392384856165240083…75365784571932835839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.939 × 10⁹⁹(100-digit number)

19392384856165240083…75365784571932835841

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

3.878 × 10⁹⁹(100-digit number)

38784769712330480166…50731569143865671679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.878 × 10⁹⁹(100-digit number)

38784769712330480166…50731569143865671681

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

7.756 × 10⁹⁹(100-digit number)

77569539424660960333…01463138287731343359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.756 × 10⁹⁹(100-digit number)

77569539424660960333…01463138287731343361

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 #1,158,790

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