Block #356,218

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 3:13:24 PM · Difficulty 10.3733 · 6,461,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

782d6fddcee065a1413d23c8f5823f4ce78273c42d67de4826b615e5124f7cb6

View on Chainz ↗

Height

#356,218

Difficulty

10.373252

Transactions

Size

756 B

Version

Bits

0a5f8d75

Nonce

16,075

Timestamp

1/12/2014, 3:13:24 PM

Confirmations

6,461,200

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

86274a11264bac712597a44e04ee6e0596a76ff84a2f395656b06b55cbf8ac85

Transactions (2)

Coinbase8dfa4f0afecf3e…f1627a28c56f61

1 in → 2 out9.2900 XPM140 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

f5f4e1abe91f38…9725ce2ba8d4ad

3 in → 2 out418.5139 XPM522 B

AcKDsk74…xxJvgev9 ALZc4CLo…aE1G3w54

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.

2.537 × 10¹⁰⁴(105-digit number)

25376925921562743277…92497731207635188479

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

2.537 × 10¹⁰⁴(105-digit number)

25376925921562743277…92497731207635188479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.537 × 10¹⁰⁴(105-digit number)

25376925921562743277…92497731207635188481

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

5.075 × 10¹⁰⁴(105-digit number)

50753851843125486555…84995462415270376959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.075 × 10¹⁰⁴(105-digit number)

50753851843125486555…84995462415270376961

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

1.015 × 10¹⁰⁵(106-digit number)

10150770368625097311…69990924830540753919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.015 × 10¹⁰⁵(106-digit number)

10150770368625097311…69990924830540753921

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

2.030 × 10¹⁰⁵(106-digit number)

20301540737250194622…39981849661081507839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.030 × 10¹⁰⁵(106-digit number)

20301540737250194622…39981849661081507841

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

4.060 × 10¹⁰⁵(106-digit number)

40603081474500389244…79963699322163015679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.060 × 10¹⁰⁵(106-digit number)

40603081474500389244…79963699322163015681

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 #356,218

Cookie Preferences