Block #349,069

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/8/2014, 4:36:35 AM · Difficulty 10.2694 · 6,459,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb49a0a87d9f7d7649c5891e4ba4f6c3889f3a08eebb41b89e9b66ca520c2408

View on Chainz ↗

Height

#349,069

Difficulty

10.269352

Transactions

Size

1.59 KB

Version

Bits

0a44f43b

Nonce

45,240

Timestamp

1/8/2014, 4:36:35 AM

Confirmations

6,459,107

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

3c988ac3e0b9416c2d0fae5d63ecf829d4565fadd63558c5bf092af34f80723c

Transactions (3)

Coinbase99b2514ac9b096…454008c63b2d17

1 in → 1 out9.5000 XPM110 B

AeKNrjNj…1NEq95Ta

3ad219e95a8b18…be3c61e0285c60

6 in → 13 out39.8732 XPM1.17 KB

AWP3nWpc…wKY1EyHx AeKNrjNj…1NEq95Ta Aadjczru…WXPUazmh AVnfbCeS…wU5T1Pkc AJzotVt1…n2DypEMR

12cd6d30c77fe5…73f5b96f0dbbae

1 in → 2 out2.5125 XPM227 B

AKK29wvS…NMfR6nq9 Ac8NFngj…g41Yxi6P

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.

2.071 × 10⁹⁹(100-digit number)

20714936285999451037…10065526343639574799

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

2.071 × 10⁹⁹(100-digit number)

20714936285999451037…10065526343639574799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.071 × 10⁹⁹(100-digit number)

20714936285999451037…10065526343639574801

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

4.142 × 10⁹⁹(100-digit number)

41429872571998902074…20131052687279149599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.142 × 10⁹⁹(100-digit number)

41429872571998902074…20131052687279149601

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

8.285 × 10⁹⁹(100-digit number)

82859745143997804148…40262105374558299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.285 × 10⁹⁹(100-digit number)

82859745143997804148…40262105374558299201

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

1.657 × 10¹⁰⁰(101-digit number)

16571949028799560829…80524210749116598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.657 × 10¹⁰⁰(101-digit number)

16571949028799560829…80524210749116598401

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

3.314 × 10¹⁰⁰(101-digit number)

33143898057599121659…61048421498233196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.314 × 10¹⁰⁰(101-digit number)

33143898057599121659…61048421498233196801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.628 × 10¹⁰⁰(101-digit number)

66287796115198243319…22096842996466393599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #349,069

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