Block #3,505,219

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2020, 11:29:33 AM · Difficulty 10.9305 · 3,336,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c1be565cdfaf0f4c31f7d6ee642cb5c17aef9daed6dffe66a363a488a2a86bb

View on Chainz ↗

Height

#3,505,219

Difficulty

10.930511

Transactions

Size

14.73 KB

Version

Bits

0aee35fe

Nonce

923,692,620

Timestamp

1/8/2020, 11:29:33 AM

Confirmations

3,336,059

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

d6c686e8d4808fa390853bac9b7cf6594230bbf63a7930616cc607e510894b6c

Transactions (3)

Coinbase46faf063f3d41a…f9f359135e374a

1 in → 1 out8.5200 XPM110 B

ASiq2qtK…VMhmk7yL

481cd33bd52083…24454dd1203a60

50 in → 1 out199.9200 XPM7.26 KB

ALcTQaSP…1C5Yf2Zi

155bc6c5ba09e7…961052973faa13

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

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.

7.297 × 10⁹⁸(99-digit number)

72976846434293845984…82248963236087070719

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

7.297 × 10⁹⁸(99-digit number)

72976846434293845984…82248963236087070719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.297 × 10⁹⁸(99-digit number)

72976846434293845984…82248963236087070721

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

1.459 × 10⁹⁹(100-digit number)

14595369286858769196…64497926472174141439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.459 × 10⁹⁹(100-digit number)

14595369286858769196…64497926472174141441

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

2.919 × 10⁹⁹(100-digit number)

29190738573717538393…28995852944348282879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.919 × 10⁹⁹(100-digit number)

29190738573717538393…28995852944348282881

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

5.838 × 10⁹⁹(100-digit number)

58381477147435076787…57991705888696565759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.838 × 10⁹⁹(100-digit number)

58381477147435076787…57991705888696565761

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

1.167 × 10¹⁰⁰(101-digit number)

11676295429487015357…15983411777393131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.167 × 10¹⁰⁰(101-digit number)

11676295429487015357…15983411777393131521

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 #3,505,219

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