Block #276,113

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 12:54:37 AM · Difficulty 9.9624 · 6,534,459 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2dfc1357bd541485594f3fd449f394c936de6fe51eeb191a6f7e13759e0b907

View on Chainz ↗

Height

#276,113

Difficulty

9.962417

Transactions

Size

1.15 KB

Version

Bits

09f660f9

Nonce

101,416

Timestamp

11/27/2013, 12:54:37 AM

Confirmations

6,534,459

Mined by

⛏️ P2SHAMjFDTvzj6AwcfM988ALARKaxSAQY3YWd7

Merkle Root

54931bbe5c2011cd0f4c6457b85c901536ab644ba6f769ff7be14d8f061535a0

Transactions (4)

Coinbase91a42333be139b…0b7de8655b5597

1 in → 1 out10.0900 XPM109 B

AMjFDTvz…AQY3YWd7

dc4965a4c897b1…d66813cac9aa28

1 in → 2 out100.6880 XPM226 B

ARZW78xy…4ca4CcM3 AdZXbM5f…mz7rhprX

7211499384e84c…2bc6bbf9444ea5

3 in → 2 out30.5696 XPM521 B

AREaYyFH…BMLN62DF ANhRcNzY…Mj3ShNFR

cb23a6ca2633eb…59831e87e23668

1 in → 2 out2.6595 XPM226 B

AR2XnKEr…eUyCwEd5 ASWywp1A…mgWVwpMt

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.

5.638 × 10⁹⁷(98-digit number)

56384000784286689103…13991718680484063039

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

5.638 × 10⁹⁷(98-digit number)

56384000784286689103…13991718680484063039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.638 × 10⁹⁷(98-digit number)

56384000784286689103…13991718680484063041

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

1.127 × 10⁹⁸(99-digit number)

11276800156857337820…27983437360968126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.127 × 10⁹⁸(99-digit number)

11276800156857337820…27983437360968126081

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

2.255 × 10⁹⁸(99-digit number)

22553600313714675641…55966874721936252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.255 × 10⁹⁸(99-digit number)

22553600313714675641…55966874721936252161

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

4.510 × 10⁹⁸(99-digit number)

45107200627429351282…11933749443872504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.510 × 10⁹⁸(99-digit number)

45107200627429351282…11933749443872504321

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

9.021 × 10⁹⁸(99-digit number)

90214401254858702565…23867498887745008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.021 × 10⁹⁸(99-digit number)

90214401254858702565…23867498887745008641

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 #276,113

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