Block #356,824

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 12:08:15 AM · Difficulty 10.3825 · 6,445,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27043f9216fdc8cda7b43341ef52de15355a4c3df47d88f6b7a56ca08d8c2f0a

View on Chainz ↗

Height

#356,824

Difficulty

10.382532

Transactions

Size

2.51 KB

Version

Bits

0a61ed9a

Nonce

639,193

Timestamp

1/13/2014, 12:08:15 AM

Confirmations

6,445,766

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

845ccfc6e774a8e085c493d2977c1fb65ecf4afe2d61633c564684aa4cd3528b

Transactions (5)

Coinbase18686414e75aa8…10d3f91747958f

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

fabaabdaca341b…8cea50bb9ff6da

10 in → 8 out21.7785 XPM1.65 KB

AS4VJ5qj…RTqSGYWL AeKNrjNj…1NEq95Ta AU33azxW…XQi4hEAP AceJi6uL…i6oUdrUA ATE8kUTd…Fdv2WBkq

57d1b1490ce010…efb8da19982313

1 in → 2 out3.7390 XPM225 B

AdKTGQuv…kSYdnT8S ARFnixLk…xnDYSkcZ

ec8ce3f8c5e790…97771024a4b990

1 in → 2 out2.4204 XPM225 B

AXhHQ9YS…k9aMEuj3 AGGreT5d…Aya98S11

e729b2e7245c20…f733c94200ab51

1 in → 2 out1.1518 XPM227 B

AJHMeUzo…o5EQTvMg AGcesWqW…nrgs7hrz

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.

3.775 × 10¹⁰⁰(101-digit number)

37752067617425956509…64658781373508377599

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

3.775 × 10¹⁰⁰(101-digit number)

37752067617425956509…64658781373508377599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.775 × 10¹⁰⁰(101-digit number)

37752067617425956509…64658781373508377601

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

7.550 × 10¹⁰⁰(101-digit number)

75504135234851913019…29317562747016755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.550 × 10¹⁰⁰(101-digit number)

75504135234851913019…29317562747016755201

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

1.510 × 10¹⁰¹(102-digit number)

15100827046970382603…58635125494033510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.510 × 10¹⁰¹(102-digit number)

15100827046970382603…58635125494033510401

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

3.020 × 10¹⁰¹(102-digit number)

30201654093940765207…17270250988067020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.020 × 10¹⁰¹(102-digit number)

30201654093940765207…17270250988067020801

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

6.040 × 10¹⁰¹(102-digit number)

60403308187881530415…34540501976134041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.040 × 10¹⁰¹(102-digit number)

60403308187881530415…34540501976134041601

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