Block #346,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 3:00:44 PM · Difficulty 10.2272 · 6,478,231 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7890a6917e81d8e2a36b69e3b2f3325a0f09edec37ab4c22f46ec2976dd9956b

View on Chainz ↗

Height

#346,532

Difficulty

10.227240

Transactions

Size

1.08 KB

Version

Bits

0a3a2c6a

Nonce

344,685

Timestamp

1/6/2014, 3:00:44 PM

Confirmations

6,478,231

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e4d16d6c1c0a5c546ab72b003686b7f7c812e5d1367a21bc1f5b69febef57eab

Transactions (5)

Coinbase20ba8bec528b0d…5c27a4bf8d0be2

1 in → 1 out9.5900 XPM110 B

AeKNrjNj…1NEq95Ta

f8bc43e33b63d2…1e7f651d9306c1

1 in → 2 out9.6400 XPM227 B

AHe4gsB8…xmjqevKt AHaJREbt…CHQhwftr

4e91628709832c…f089cbe8e19579

1 in → 2 out9.6400 XPM226 B

ANuxHY92…mnhYehab AW7HXYN5…5bCrGJQL

28fce0a6ffcdc7…7dcbaf976b106b

1 in → 2 out9.6400 XPM227 B

ANz39bZR…PszfywGJ AcseuZRr…2T3Ex5a8

c558c452549ea1…39fb46ceddf8d5

1 in → 2 out8.6268 XPM226 B

AZBiQGed…YS9Xi3h3 AU7mPuCX…XfwXUJwF

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.

4.043 × 10¹⁰²(103-digit number)

40437033126063751491…35062992592017609759

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

4.043 × 10¹⁰²(103-digit number)

40437033126063751491…35062992592017609759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.043 × 10¹⁰²(103-digit number)

40437033126063751491…35062992592017609761

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

8.087 × 10¹⁰²(103-digit number)

80874066252127502983…70125985184035219519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.087 × 10¹⁰²(103-digit number)

80874066252127502983…70125985184035219521

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

1.617 × 10¹⁰³(104-digit number)

16174813250425500596…40251970368070439039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.617 × 10¹⁰³(104-digit number)

16174813250425500596…40251970368070439041

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

3.234 × 10¹⁰³(104-digit number)

32349626500851001193…80503940736140878079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.234 × 10¹⁰³(104-digit number)

32349626500851001193…80503940736140878081

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

6.469 × 10¹⁰³(104-digit number)

64699253001702002386…61007881472281756159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.469 × 10¹⁰³(104-digit number)

64699253001702002386…61007881472281756161

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 #346,532

Cookie Preferences