Block #282,874

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 1:09:58 PM · Difficulty 9.9800 · 6,531,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9964964725118b03dab455c2f27d504842a803c8bf8042d1956f458580edff79

View on Chainz ↗

Height

#282,874

Difficulty

9.980011

Transactions

Size

2.67 KB

Version

Bits

09fae1f8

Nonce

27,215

Timestamp

11/29/2013, 1:09:58 PM

Confirmations

6,531,443

Mined by

⛏️ P2SHAM9ttoa79W4XaD2zgy1kevBCXHWFfcoHsY

Merkle Root

2c699a781d38b059ea9a01f43487e9e174b6fdc480118d5b0883d21c905a3cdb

Transactions (5)

Coinbase0142e9a0782954…374f311bd05824

1 in → 1 out10.0800 XPM109 B

AM9ttoa7…WFfcoHsY

79cdec4a2f88cf…51233afb33ea72

7 in → 2 out3.1218 XPM1.09 KB

AaUERP1W…wucDzMxV AT9HjzFz…QU5aVhCW

df113c3544b9e3…44559f8bb0896a

3 in → 2 out4.0150 XPM523 B

AUXBzj5U…7z6819qT AVaPpEqs…TJ1YVw7T

15e028db623692…b6fcc55750c0fa

1 in → 2 out1.2960 XPM226 B

AXtWJcJV…QdbSzzTC AbM2ihf2…nQ5eccn1

e94375048572b2…2d8a0ce1e6336a

4 in → 2 out1.0146 XPM669 B

AYqPbKmV…AMYeRt2x AeomYLfa…LU4ekaBw

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.

1.003 × 10⁹⁴(95-digit number)

10036320360399843963…74066405150056820479

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

1.003 × 10⁹⁴(95-digit number)

10036320360399843963…74066405150056820479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10⁹⁴(95-digit number)

10036320360399843963…74066405150056820481

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

2.007 × 10⁹⁴(95-digit number)

20072640720799687927…48132810300113640959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.007 × 10⁹⁴(95-digit number)

20072640720799687927…48132810300113640961

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

4.014 × 10⁹⁴(95-digit number)

40145281441599375855…96265620600227281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.014 × 10⁹⁴(95-digit number)

40145281441599375855…96265620600227281921

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

8.029 × 10⁹⁴(95-digit number)

80290562883198751711…92531241200454563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.029 × 10⁹⁴(95-digit number)

80290562883198751711…92531241200454563841

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

1.605 × 10⁹⁵(96-digit number)

16058112576639750342…85062482400909127679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #282,874

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