Block #361,437

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 2:01:45 AM · Difficulty 10.4051 · 6,463,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5f5b9d6a25653077ccc7dc91d8556fb8cf465043f96c87472d1faba2175b9d5

View on Chainz ↗

Height

#361,437

Difficulty

10.405076

Transactions

Size

880 B

Version

Bits

0a67b310

Nonce

22,739

Timestamp

1/16/2014, 2:01:45 AM

Confirmations

6,463,374

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c5d999849ba0956f433c2e875455a1349655bafc6b8273f4dbfca8c31811da33

Transactions (4)

Coinbase030275df5c89a1…3232a70d7612b8

1 in → 1 out9.2500 XPM109 B

AeKNrjNj…1NEq95Ta

782e43410666b8…4d76718d200238

1 in → 2 out7.1668 XPM227 B

Aa7SCWJe…EEUE2cR6 AH8hPofR…y7cHvL7w

94090bc50fd927…78a9cc0149fc36

1 in → 2 out3.1608 XPM225 B

AYXiQEyP…myu8sEHZ AQWmv8ZV…N6WyBFfi

a3e5fe71f7e349…af34db49a0263b

1 in → 2 out1.1662 XPM226 B

AVjDKK78…bM5FERyB AYQDWrKR…6dxveeRe

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.

1.301 × 10¹⁰³(104-digit number)

13018933682922872870…15068729419222153599

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

1.301 × 10¹⁰³(104-digit number)

13018933682922872870…15068729419222153599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.301 × 10¹⁰³(104-digit number)

13018933682922872870…15068729419222153601

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

2.603 × 10¹⁰³(104-digit number)

26037867365845745741…30137458838444307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.603 × 10¹⁰³(104-digit number)

26037867365845745741…30137458838444307201

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

5.207 × 10¹⁰³(104-digit number)

52075734731691491482…60274917676888614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.207 × 10¹⁰³(104-digit number)

52075734731691491482…60274917676888614401

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

1.041 × 10¹⁰⁴(105-digit number)

10415146946338298296…20549835353777228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.041 × 10¹⁰⁴(105-digit number)

10415146946338298296…20549835353777228801

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

2.083 × 10¹⁰⁴(105-digit number)

20830293892676596593…41099670707554457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.083 × 10¹⁰⁴(105-digit number)

20830293892676596593…41099670707554457601

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 #361,437

Cookie Preferences