Block #334,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 9:10:44 PM · Difficulty 10.1605 · 6,481,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

251ec21997abfd6df4f829112d4c6be1b659b7f46ac0163e35101911e517397f

View on Chainz ↗

Height

#334,937

Difficulty

10.160524

Transactions

Size

1.22 KB

Version

Bits

0a29181e

Nonce

204,841

Timestamp

12/29/2013, 9:10:44 PM

Confirmations

6,481,210

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c6453fbe445b218e2a0f4236b8273d02b8dc57dfce124299e55943748dc580a9

Transactions (5)

Coinbase84c2ed113bfa5d…c8d43053b31a91

1 in → 1 out9.7100 XPM110 B

AeKNrjNj…1NEq95Ta

a5195053128b6d…9f4855f899af08

1 in → 2 out5.5081 XPM225 B

ALQx59LV…R8LoHHSH AQdi7bqD…bp9ePC7F

45f2e7537ba103…01fc49306a80b5

1 in → 2 out2.7787 XPM226 B

ALSBYPdx…z3FZQcBW AZeuLEoS…ErgE4MTN

31ecf4044e8eea…62e8423e87bc66

1 in → 2 out1.1924 XPM226 B

AN8UKtJp…R9L3jZ3E AX9vr9YZ…H2scRbPH

b0731805a3359b…cedafc1f72a532

2 in → 2 out1.0270 XPM375 B

AeWsehaJ…Ucp9DhHw AWxqMmno…m7er1kai

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.

5.927 × 10¹⁰⁰(101-digit number)

59274207922099377075…67896971519720777319

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

5.927 × 10¹⁰⁰(101-digit number)

59274207922099377075…67896971519720777319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.927 × 10¹⁰⁰(101-digit number)

59274207922099377075…67896971519720777321

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

1.185 × 10¹⁰¹(102-digit number)

11854841584419875415…35793943039441554639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.185 × 10¹⁰¹(102-digit number)

11854841584419875415…35793943039441554641

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

2.370 × 10¹⁰¹(102-digit number)

23709683168839750830…71587886078883109279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.370 × 10¹⁰¹(102-digit number)

23709683168839750830…71587886078883109281

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

4.741 × 10¹⁰¹(102-digit number)

47419366337679501660…43175772157766218559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.741 × 10¹⁰¹(102-digit number)

47419366337679501660…43175772157766218561

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

9.483 × 10¹⁰¹(102-digit number)

94838732675359003321…86351544315532437119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.483 × 10¹⁰¹(102-digit number)

94838732675359003321…86351544315532437121

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 #334,937

Cookie Preferences