Block #1,653,799

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/30/2016, 11:19:22 AM · Difficulty 10.7656 · 5,185,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7024574e1be51394b7dc25f25105cbfdfa0de5b33d41fe6a3cc485e78569b938

View on Chainz ↗

Height

#1,653,799

Difficulty

10.765582

Transactions

Size

1.75 KB

Version

Bits

0ac3fd33

Nonce

538,317,027

Timestamp

6/30/2016, 11:19:22 AM

Confirmations

5,185,477

Mined by

⛏️ P2SHAdr41VfN9CEyHDA21tiRsuLHj2L97rxARj

Merkle Root

0b89b8ba6b1abef1558161e39f77beb71cbd8cf4b4e3d165518b3b77829b689c

Transactions (2)

Coinbasedf4177713297ae…c0e1f356ea793c

1 in → 1 out8.6300 XPM110 B

Adr41VfN…L97rxARj

f6ea6b708f88ba…9051b5b482e4fc

10 in → 3 out660.2242 XPM1.56 KB

AToabZvF…24kuoA4M Ab73za2X…QCvdLNC4 AQcjeddP…AoqhXrhG

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.

1.608 × 10⁹⁵(96-digit number)

16086792541178065890…70930365326835309599

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

1.608 × 10⁹⁵(96-digit number)

16086792541178065890…70930365326835309599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.608 × 10⁹⁵(96-digit number)

16086792541178065890…70930365326835309601

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

3.217 × 10⁹⁵(96-digit number)

32173585082356131781…41860730653670619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.217 × 10⁹⁵(96-digit number)

32173585082356131781…41860730653670619201

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

6.434 × 10⁹⁵(96-digit number)

64347170164712263562…83721461307341238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.434 × 10⁹⁵(96-digit number)

64347170164712263562…83721461307341238401

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

1.286 × 10⁹⁶(97-digit number)

12869434032942452712…67442922614682476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.286 × 10⁹⁶(97-digit number)

12869434032942452712…67442922614682476801

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

2.573 × 10⁹⁶(97-digit number)

25738868065884905424…34885845229364953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.573 × 10⁹⁶(97-digit number)

25738868065884905424…34885845229364953601

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 #1,653,799

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