Block #2,266,010

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/24/2017, 3:13:32 PM · Difficulty 10.9515 · 4,564,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4960aa2b209a6546beb7db1af7093fae16ece19d9a2f0d9caf489b8ab00c0246

View on Chainz ↗

Height

#2,266,010

Difficulty

10.951521

Transactions

Size

1.08 KB

Version

Bits

0af396dc

Nonce

915,020,307

Timestamp

8/24/2017, 3:13:32 PM

Confirmations

4,564,883

Mined by

⛏️ P2SHAUXm22JcgzMMbFWM1JJuRdTvUSB1vuBXoa

Merkle Root

e576a9d01614673d1e5686f859e49238b7a9c80706a1f363dd7710d08798e425

Transactions (5)

Coinbase62dfa8625d292b…8b7183d696a50a

1 in → 1 out8.3600 XPM110 B

AUXm22Jc…B1vuBXoa

35e6d6cff0133a…ca1d8fd9757f8c

1 in → 2 out122411.1080 XPM226 B

AZ38GrUc…DtXVJXTt AeTK2F54…XkjqoxT8

22645cbf20e3ee…9006eaf2bf11d9

1 in → 2 out2969.9900 XPM226 B

AGGwzESb…C2XD33vS APCLwsZN…Y9nxkbdb

05fabdf90ba900…46e7c62f3d0655

1 in → 2 out2969.9900 XPM226 B

AJt8GRK7…Cicth62B AHiuZ7aX…qLfT8w8v

a6c57dc903d9cf…e062502cd7b287

1 in → 2 out584.1800 XPM226 B

ATZTuGLX…vjX5EWx8 AMZzAxdf…bStSqjx6

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.

4.363 × 10⁹⁷(98-digit number)

43637424743146611652…89686653292364697599

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

4.363 × 10⁹⁷(98-digit number)

43637424743146611652…89686653292364697599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.363 × 10⁹⁷(98-digit number)

43637424743146611652…89686653292364697601

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

8.727 × 10⁹⁷(98-digit number)

87274849486293223305…79373306584729395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.727 × 10⁹⁷(98-digit number)

87274849486293223305…79373306584729395201

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

1.745 × 10⁹⁸(99-digit number)

17454969897258644661…58746613169458790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.745 × 10⁹⁸(99-digit number)

17454969897258644661…58746613169458790401

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

3.490 × 10⁹⁸(99-digit number)

34909939794517289322…17493226338917580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.490 × 10⁹⁸(99-digit number)

34909939794517289322…17493226338917580801

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

6.981 × 10⁹⁸(99-digit number)

69819879589034578644…34986452677835161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.981 × 10⁹⁸(99-digit number)

69819879589034578644…34986452677835161601

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 #2,266,010

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