Block #417,034

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 8:58:46 PM · Difficulty 10.3953 · 6,407,627 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e96c12a830d4c14c104ba9dbe95f8e6f620d98b9bbfbc18ed3f21217aa0dd134

View on Chainz ↗

Height

#417,034

Difficulty

10.395311

Transactions

Size

576 B

Version

Bits

0a653312

Nonce

200,794

Timestamp

2/23/2014, 8:58:46 PM

Confirmations

6,407,627

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

48b466e597386691e4e2bb2b3fae02b08ed0101255bc0e7da3067432c7ffc6c9

Transactions (2)

Coinbasee33a41249dcdb2…684f1a1d207352

1 in → 1 out9.2500 XPM110 B

AeKNrjNj…1NEq95Ta

4176cdcc692474…846284dac2bcfc

2 in → 2 out3.0922 XPM374 B

AUrBZDxq…ycvbyXPS AURgSAim…x7AJFFXo

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.

2.760 × 10¹⁰⁰(101-digit number)

27602336944032977802…70846035699908071679

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

2.760 × 10¹⁰⁰(101-digit number)

27602336944032977802…70846035699908071679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.760 × 10¹⁰⁰(101-digit number)

27602336944032977802…70846035699908071681

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

5.520 × 10¹⁰⁰(101-digit number)

55204673888065955605…41692071399816143359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.520 × 10¹⁰⁰(101-digit number)

55204673888065955605…41692071399816143361

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

1.104 × 10¹⁰¹(102-digit number)

11040934777613191121…83384142799632286719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.104 × 10¹⁰¹(102-digit number)

11040934777613191121…83384142799632286721

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

2.208 × 10¹⁰¹(102-digit number)

22081869555226382242…66768285599264573439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.208 × 10¹⁰¹(102-digit number)

22081869555226382242…66768285599264573441

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

4.416 × 10¹⁰¹(102-digit number)

44163739110452764484…33536571198529146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.416 × 10¹⁰¹(102-digit number)

44163739110452764484…33536571198529146881

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 #417,034

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