Block #352,694

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 12:13:51 PM · Difficulty 10.3112 · 6,458,998 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59b79452bd86162a80b60c19fd799bd35613d5504d00b404c7ead655b72d59cd

View on Chainz ↗

Height

#352,694

Difficulty

10.311239

Transactions

Size

1.29 KB

Version

Bits

0a4fad5c

Nonce

13,414

Timestamp

1/10/2014, 12:13:51 PM

Confirmations

6,458,998

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

202a81ff383e2ac855ed55591e763c362e5e882a9843fa1fa43681743dc2a216

Transactions (4)

Coinbase30e1b782196368…840e0d5e3e2a35

1 in → 2 out9.4200 XPM137 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

ccdf1e8f952410…070d119308172b

3 in → 1 out0.9108 XPM487 B

AWxsN2vJ…eaiBAqmW

08d3d9ee6f75cb…8451f658866ac7

1 in → 2 out4.3959 XPM227 B

AQnWMim4…qG8rjHWB AaiAQoiA…L6Q8wU2w

0b708980f6c078…487e64ce6bca64

2 in → 2 out5.0254 XPM374 B

AT5oTsET…Pi5H6raU AVwXLN4a…7Xa69RTV

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.

6.515 × 10¹⁰²(103-digit number)

65154229929674569953…60272708200522475279

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

6.515 × 10¹⁰²(103-digit number)

65154229929674569953…60272708200522475279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.515 × 10¹⁰²(103-digit number)

65154229929674569953…60272708200522475281

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

1.303 × 10¹⁰³(104-digit number)

13030845985934913990…20545416401044950559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.303 × 10¹⁰³(104-digit number)

13030845985934913990…20545416401044950561

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

2.606 × 10¹⁰³(104-digit number)

26061691971869827981…41090832802089901119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.606 × 10¹⁰³(104-digit number)

26061691971869827981…41090832802089901121

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

5.212 × 10¹⁰³(104-digit number)

52123383943739655962…82181665604179802239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.212 × 10¹⁰³(104-digit number)

52123383943739655962…82181665604179802241

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

1.042 × 10¹⁰⁴(105-digit number)

10424676788747931192…64363331208359604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.042 × 10¹⁰⁴(105-digit number)

10424676788747931192…64363331208359604481

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 #352,694

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