Block #355,701

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 7:54:06 AM · Difficulty 10.3631 · 6,455,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a18d2c95746c3106ac62e428b0ab4bb7b4919e38a13596669b5c774da6434a56

View on Chainz ↗

Height

#355,701

Difficulty

10.363070

Transactions

Size

1.25 KB

Version

Bits

0a5cf220

Nonce

265,388

Timestamp

1/12/2014, 7:54:06 AM

Confirmations

6,455,036

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

76ef55d4374e62455d6a1858196f05e1afeb701e73b5f76fe60117f6a0f8d6b7

Transactions (4)

Coinbase612e2defd386c5…25c8ef40320939

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

3d375d819f8847…afd75520161b0f

3 in → 2 out7.9459 XPM521 B

AXubF3FJ…YXrsLUMP ASHGTYM6…wmD9y4hg

956be40330de58…fe86f0e2174ca4

1 in → 1 out2.9901 XPM191 B

Adr3Jckh…d94vX9ht

baf3e62baaa50f…783d64b371c1e2

2 in → 2 out2.2619 XPM372 B

AUmrvvFj…v6weqdMx ASc8QVRF…1U8ePxyT

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.

1.951 × 10⁹⁴(95-digit number)

19516693177705191923…23958601790886523519

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

1.951 × 10⁹⁴(95-digit number)

19516693177705191923…23958601790886523519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.951 × 10⁹⁴(95-digit number)

19516693177705191923…23958601790886523521

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

3.903 × 10⁹⁴(95-digit number)

39033386355410383847…47917203581773047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.903 × 10⁹⁴(95-digit number)

39033386355410383847…47917203581773047041

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

7.806 × 10⁹⁴(95-digit number)

78066772710820767694…95834407163546094079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.806 × 10⁹⁴(95-digit number)

78066772710820767694…95834407163546094081

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

1.561 × 10⁹⁵(96-digit number)

15613354542164153538…91668814327092188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.561 × 10⁹⁵(96-digit number)

15613354542164153538…91668814327092188161

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

3.122 × 10⁹⁵(96-digit number)

31226709084328307077…83337628654184376319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.122 × 10⁹⁵(96-digit number)

31226709084328307077…83337628654184376321

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 #355,701

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