Block #336,643

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 2:41:29 AM · Difficulty 10.1419 · 6,459,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c709d1facfc89d1e4d17ae21d454155d338e9332438072e52fcebd616a4bb7bc

View on Chainz ↗

Height

#336,643

Difficulty

10.141897

Transactions

Size

9.87 KB

Version

Bits

0a245357

Nonce

177,874

Timestamp

12/31/2013, 2:41:29 AM

Confirmations

6,459,788

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ae84d3551694f7efbc1aeed507700c5335a6be05abae0dd6bf13964f1dd9982c

Transactions (5)

Coinbase5aac76fa8f2553…e53e4a84cf4289

1 in → 1 out9.8400 XPM110 B

AeKNrjNj…1NEq95Ta

c26a8c1e9d8fe3…4959ba7f4becfd

6 in → 16 out49.1728 XPM1.24 KB

ARZCtjhg…WhMk8pJQ AcpNGovK…Ph5h4fjC AZCf3PAA…B86Zhw54 AWJGxHGw…FnzsgZqe AJHGrbLZ…FNHzsjtJ

ee870a2e7b9704…4865dc798d2591

55 in → 1 out17.4323 XPM7.99 KB

AJAYG6kY…VvpkjrVf

a87f2655460ba0…6bddc21ad02a71

1 in → 2 out5.5157 XPM225 B

AGAMt16a…4LVibYA3 AHzAXTeS…um5bgWHC

3a4bb89bbddf12…22cefa291ed482

1 in → 2 out3.0000 XPM224 B

AQaKf3gr…x5V5aSU6 AKmxBBzd…AHmu4uiE

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.

3.302 × 10⁹⁹(100-digit number)

33025445194603121999…20403504739472998399

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

3.302 × 10⁹⁹(100-digit number)

33025445194603121999…20403504739472998399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.302 × 10⁹⁹(100-digit number)

33025445194603121999…20403504739472998401

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

6.605 × 10⁹⁹(100-digit number)

66050890389206243998…40807009478945996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.605 × 10⁹⁹(100-digit number)

66050890389206243998…40807009478945996801

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

1.321 × 10¹⁰⁰(101-digit number)

13210178077841248799…81614018957891993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.321 × 10¹⁰⁰(101-digit number)

13210178077841248799…81614018957891993601

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

2.642 × 10¹⁰⁰(101-digit number)

26420356155682497599…63228037915783987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.642 × 10¹⁰⁰(101-digit number)

26420356155682497599…63228037915783987201

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

5.284 × 10¹⁰⁰(101-digit number)

52840712311364995198…26456075831567974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.284 × 10¹⁰⁰(101-digit number)

52840712311364995198…26456075831567974401

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