Block #2,079,326

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/20/2017, 10:37:13 AM · Difficulty 10.8592 · 4,747,232 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31ab6e69350161ea226c81e10bd7532f26600c39a4b23adb261946537131acee

View on Chainz ↗

Height

#2,079,326

Difficulty

10.859243

Transactions

Size

871 B

Version

Bits

0adbf756

Nonce

415,651,822

Timestamp

4/20/2017, 10:37:13 AM

Confirmations

4,747,232

Mined by

⛏️ P2SHAWg25KgPfyVShkGcZRiGQpdo4MzRtHXpSU

Merkle Root

5b205a4b4d37eec4ad8d8f8e257401a7bad397809118d60f4ea18262ae493eed

Transactions (2)

Coinbasef78dd1c300d704…b2e7d8b5df0f78

1 in → 1 out8.4900 XPM109 B

AWg25KgP…zRtHXpSU

1849b2333da04c…df98859bf369c8

4 in → 2 out2374.2200 XPM672 B

AXoGTmVb…w1f3iQWM AZYKyJBX…U2t99o2L

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.

5.111 × 10⁹³(94-digit number)

51118306342038163215…97349786062907967939

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

5.111 × 10⁹³(94-digit number)

51118306342038163215…97349786062907967939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.111 × 10⁹³(94-digit number)

51118306342038163215…97349786062907967941

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

1.022 × 10⁹⁴(95-digit number)

10223661268407632643…94699572125815935879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.022 × 10⁹⁴(95-digit number)

10223661268407632643…94699572125815935881

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

2.044 × 10⁹⁴(95-digit number)

20447322536815265286…89399144251631871759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.044 × 10⁹⁴(95-digit number)

20447322536815265286…89399144251631871761

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

4.089 × 10⁹⁴(95-digit number)

40894645073630530572…78798288503263743519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.089 × 10⁹⁴(95-digit number)

40894645073630530572…78798288503263743521

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

8.178 × 10⁹⁴(95-digit number)

81789290147261061144…57596577006527487039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.178 × 10⁹⁴(95-digit number)

81789290147261061144…57596577006527487041

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

1.635 × 10⁹⁵(96-digit number)

16357858029452212228…15193154013054974079

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 #2,079,326

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