Block #2,110,355

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2017, 5:28:05 PM · Difficulty 10.9026 · 4,731,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ca6952c26e9f8c45bc5d9ff5015fc367b518a22bcfefa5ae2fb84c1ee4c2d2c

View on Chainz ↗

Height

#2,110,355

Difficulty

10.902601

Transactions

Size

428 B

Version

Bits

0ae710d7

Nonce

1,335,974,590

Timestamp

5/10/2017, 5:28:05 PM

Confirmations

4,731,544

Mined by

⛏️ P2SHAQVj7FpGA8xYEHSmrCMHsf3My191ncdyZ5

Merkle Root

0c30dc67b2bbac6d7a4509bc692861491fcdf013f627423ac06b9e14c8fcff0f

Transactions (2)

Coinbase4e72abe09ab738…11339777d447ab

1 in → 1 out8.4100 XPM110 B

AQVj7FpG…91ncdyZ5

e46ac91ec5aae4…e2df70a9c930de

1 in → 2 out7021.9921 XPM227 B

AKQJUnwV…mgLMEfah AGeuhrNJ…1qySk3Ej

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.

8.340 × 10⁹⁶(97-digit number)

83407277013220110084…35738089462367252479

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

8.340 × 10⁹⁶(97-digit number)

83407277013220110084…35738089462367252479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.340 × 10⁹⁶(97-digit number)

83407277013220110084…35738089462367252481

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

1.668 × 10⁹⁷(98-digit number)

16681455402644022016…71476178924734504959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.668 × 10⁹⁷(98-digit number)

16681455402644022016…71476178924734504961

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

3.336 × 10⁹⁷(98-digit number)

33362910805288044033…42952357849469009919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.336 × 10⁹⁷(98-digit number)

33362910805288044033…42952357849469009921

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

6.672 × 10⁹⁷(98-digit number)

66725821610576088067…85904715698938019839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.672 × 10⁹⁷(98-digit number)

66725821610576088067…85904715698938019841

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

1.334 × 10⁹⁸(99-digit number)

13345164322115217613…71809431397876039679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.334 × 10⁹⁸(99-digit number)

13345164322115217613…71809431397876039681

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 #2,110,355

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