Block #349,270

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/8/2014, 8:03:10 AM · Difficulty 10.2684 · 6,467,592 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a1a3f672e1c52e97e5e6c80a0a76b5742a2cb1c7e67d5857b168970c675e21b

View on Chainz ↗

Height

#349,270

Difficulty

10.268402

Transactions

Size

868 B

Version

Bits

0a44b606

Nonce

197,205

Timestamp

1/8/2014, 8:03:10 AM

Confirmations

6,467,592

Mined by

⛏️ P2SHAe1uYg8V7MyvCHfS6K5ud7obsTgWX6vjXp

Merkle Root

bfe0251ec4d8674a74e3a5aa7ca2f458f858d2d6ef89165beec952a33dc08ac6

Transactions (2)

Coinbasedd788f4a9171f3…021837ddbf7a24

1 in → 1 out9.4800 XPM109 B

Ae1uYg8V…gWX6vjXp

5935145e6baa3e…10fb7fd3cf3c33

4 in → 2 out1.3519 XPM668 B

AGUiHrXX…99nzH74G ATmyCRmE…VjVh9WL5

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.

1.960 × 10⁹⁸(99-digit number)

19601793119562978049…50915926917544657919

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

1.960 × 10⁹⁸(99-digit number)

19601793119562978049…50915926917544657919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.960 × 10⁹⁸(99-digit number)

19601793119562978049…50915926917544657921

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

3.920 × 10⁹⁸(99-digit number)

39203586239125956098…01831853835089315839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.920 × 10⁹⁸(99-digit number)

39203586239125956098…01831853835089315841

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

7.840 × 10⁹⁸(99-digit number)

78407172478251912196…03663707670178631679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.840 × 10⁹⁸(99-digit number)

78407172478251912196…03663707670178631681

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

1.568 × 10⁹⁹(100-digit number)

15681434495650382439…07327415340357263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.568 × 10⁹⁹(100-digit number)

15681434495650382439…07327415340357263361

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

3.136 × 10⁹⁹(100-digit number)

31362868991300764878…14654830680714526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.136 × 10⁹⁹(100-digit number)

31362868991300764878…14654830680714526721

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

6.272 × 10⁹⁹(100-digit number)

62725737982601529756…29309661361429053439

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 #349,270

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