Block #341,102

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/3/2014, 6:11:06 AM · Difficulty 10.1312 · 6,466,037 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14d252d3ce1f98f8f922c734f87d9f37fe247916011dfbd675ef50302ee0bd57

View on Chainz ↗

Height

#341,102

Difficulty

10.131231

Transactions

Size

1.11 KB

Version

Bits

0a21985d

Nonce

181,218

Timestamp

1/3/2014, 6:11:06 AM

Confirmations

6,466,037

Mined by

⛏️ n4aRThAG5YAjechu8kNZ5eyyVJVz1YnBVhA4Aeh1

Merkle Root

3f05d4d2f8380b872a7172e3475d7e1faa161ad1ef158f84aee2119cf74cc690

Transactions (1)

Coinbase3f05d4d2f8380b…e2119cf74cc690

1 in → 29 out9.7100 XPM1.02 KB

AG5YAjec…VhA4Aeh1 AQ8QAT3J…rCFKuVbR AP5UvYhU…vLTDwkdA AayReikY…2HAC42fs AYckRkCF…TgDe5VSp

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.

1.370 × 10⁹⁴(95-digit number)

13707845141698477490…62536415921027237559

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

1.370 × 10⁹⁴(95-digit number)

13707845141698477490…62536415921027237559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.370 × 10⁹⁴(95-digit number)

13707845141698477490…62536415921027237561

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

2.741 × 10⁹⁴(95-digit number)

27415690283396954981…25072831842054475119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.741 × 10⁹⁴(95-digit number)

27415690283396954981…25072831842054475121

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

5.483 × 10⁹⁴(95-digit number)

54831380566793909962…50145663684108950239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.483 × 10⁹⁴(95-digit number)

54831380566793909962…50145663684108950241

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

1.096 × 10⁹⁵(96-digit number)

10966276113358781992…00291327368217900479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.096 × 10⁹⁵(96-digit number)

10966276113358781992…00291327368217900481

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

2.193 × 10⁹⁵(96-digit number)

21932552226717563985…00582654736435800959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.193 × 10⁹⁵(96-digit number)

21932552226717563985…00582654736435800961

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

4.386 × 10⁹⁵(96-digit number)

43865104453435127970…01165309472871601919

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 #341,102

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