Block #3,470,336

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2019, 10:06:10 PM · Difficulty 10.9791 · 3,336,245 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed195c9fea2c3a8539d90e585066e95c6b23edc9dd342391268fda9cebf755b9

View on Chainz ↗

Height

#3,470,336

Difficulty

10.979142

Transactions

Size

5.83 KB

Version

Bits

0afaa915

Nonce

814,210,654

Timestamp

12/10/2019, 10:06:10 PM

Confirmations

3,336,245

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

153bbbcc5e144b5502c414900a8f7d7a4a2a9dbf678d7b6b885aed229383014a

Transactions (4)

Coinbase2b9ee38b8f33e3…0b7d3ac8686ccd

1 in → 1 out8.3600 XPM110 B

ASiq2qtK…VMhmk7yL

b7b1efa3265e9f…7241a7385d6298

2 in → 124 out863.5278 XPM4.42 KB

AcArjy9q…3jkKsfB2 AWySGZFv…2MYZwLyx AXQfViLn…9h3N8vtY AT8M6fHF…QuK2JQMM AMB6n3EC…HJVJSW38

747b2b7ec5165c…c77e4bb4faee69

8 in → 2 out50.1421 XPM1.03 KB

Ac46JApH…3bgULjJC ASiq2qtK…VMhmk7yL

2ea9801580676a…e2e91cffa13807

1 in → 2 out8.2700 XPM192 B

ATsGpLaK…6ivo8bfZ ASiq2qtK…VMhmk7yL

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.

4.397 × 10⁹⁵(96-digit number)

43976354728839281243…88106590535617085439

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

4.397 × 10⁹⁵(96-digit number)

43976354728839281243…88106590535617085439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.397 × 10⁹⁵(96-digit number)

43976354728839281243…88106590535617085441

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

8.795 × 10⁹⁵(96-digit number)

87952709457678562487…76213181071234170879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.795 × 10⁹⁵(96-digit number)

87952709457678562487…76213181071234170881

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

1.759 × 10⁹⁶(97-digit number)

17590541891535712497…52426362142468341759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.759 × 10⁹⁶(97-digit number)

17590541891535712497…52426362142468341761

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

3.518 × 10⁹⁶(97-digit number)

35181083783071424994…04852724284936683519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.518 × 10⁹⁶(97-digit number)

35181083783071424994…04852724284936683521

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

7.036 × 10⁹⁶(97-digit number)

70362167566142849989…09705448569873367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.036 × 10⁹⁶(97-digit number)

70362167566142849989…09705448569873367041

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 #3,470,336

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