Block #1,611,996

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/3/2016, 6:04:30 AM · Difficulty 10.6049 · 5,230,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdba7b13fb82d09b08a145a606ee065886c107928549ff0c7467c6d0faa0a7a6

View on Chainz ↗

Height

#1,611,996

Difficulty

10.604856

Transactions

Size

2.99 KB

Version

Bits

0a9ad7df

Nonce

734,231,133

Timestamp

6/3/2016, 6:04:30 AM

Confirmations

5,230,101

Mined by

⛏️ P2SHAVmJ81GkpUf7xkYXTUAVcsWYQ8X13s6x4z

Merkle Root

8dd8ad5f216e0b4ddf567754e61a733e999ec9601c6687e9be173df204f9f83b

Transactions (2)

Coinbasee24e4d171437bb…97b95212f87f8d

1 in → 1 out8.9100 XPM109 B

AVmJ81Gk…X13s6x4z

976cc85f51777c…0c0945b41f8dbe

19 in → 1 out75.9700 XPM2.79 KB

AWHNqcat…yWKiKodA

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.

1.162 × 10⁹⁶(97-digit number)

11622313194815358315…39337685808578416639

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

1.162 × 10⁹⁶(97-digit number)

11622313194815358315…39337685808578416639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.162 × 10⁹⁶(97-digit number)

11622313194815358315…39337685808578416641

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

2.324 × 10⁹⁶(97-digit number)

23244626389630716631…78675371617156833279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.324 × 10⁹⁶(97-digit number)

23244626389630716631…78675371617156833281

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

4.648 × 10⁹⁶(97-digit number)

46489252779261433263…57350743234313666559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.648 × 10⁹⁶(97-digit number)

46489252779261433263…57350743234313666561

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

9.297 × 10⁹⁶(97-digit number)

92978505558522866527…14701486468627333119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.297 × 10⁹⁶(97-digit number)

92978505558522866527…14701486468627333121

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

1.859 × 10⁹⁷(98-digit number)

18595701111704573305…29402972937254666239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.859 × 10⁹⁷(98-digit number)

18595701111704573305…29402972937254666241

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 #1,611,996

Cookie Preferences