Block #410,114

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 8:08:47 PM · Difficulty 10.4304 · 6,382,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3205f28040b489db8e038600b1be3e0363f7b98927a9aafa780aec9a525329e8

View on Chainz ↗

Height

#410,114

Difficulty

10.430389

Transactions

Size

1.83 KB

Version

Bits

0a6e2df9

Nonce

36,892

Timestamp

2/18/2014, 8:08:47 PM

Confirmations

6,382,660

Merkle Root

fcd6222314e86fd601da8c702c4119b204b45d37aae2e8ab890b5ec3697e984d

Transactions (5)

Coinbasea9dc2141ca5a84…48b1bb9139c6e3

1 in → 24 out9.2200 XPM879 B

AMW1p9oT…2TzdaZxH Acs9SHrk…QJSB8SFG AMypZdXS…5jJKu8wP AZqjMFvv…G8aw2zC8 AUDD9tmA…gJPQLnsz

5d0c5cd511fc8e…955b62abf3a9b5

1 in → 2 out4.9905 XPM227 B

AMQkxddh…4XFMqZQF AMPT3vw3…wXkRUQ12

63edc9ad24ead4…f9e6bacdf66d6b

1 in → 2 out4.9074 XPM225 B

AWWg5w3k…Mb1bnxL8 ARgpds8y…t5DAyJVT

b7fff9b34e40cd…31666aef518491

1 in → 2 out4.8447 XPM225 B

AK5eMZv7…7wDmjJxU AViXcJ2f…1WbeKgHj

56b8c9145f67b9…48755455ac3c87

1 in → 2 out2.8841 XPM225 B

AP4CANr7…2GDbyVJf AJD2MBFp…yQA75iRs

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.

4.589 × 10¹⁰⁰(101-digit number)

45895906190158643941…75069489236160103039

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

4.589 × 10¹⁰⁰(101-digit number)

45895906190158643941…75069489236160103039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.589 × 10¹⁰⁰(101-digit number)

45895906190158643941…75069489236160103041

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

9.179 × 10¹⁰⁰(101-digit number)

91791812380317287882…50138978472320206079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.179 × 10¹⁰⁰(101-digit number)

91791812380317287882…50138978472320206081

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

1.835 × 10¹⁰¹(102-digit number)

18358362476063457576…00277956944640412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.835 × 10¹⁰¹(102-digit number)

18358362476063457576…00277956944640412161

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

3.671 × 10¹⁰¹(102-digit number)

36716724952126915153…00555913889280824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.671 × 10¹⁰¹(102-digit number)

36716724952126915153…00555913889280824321

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

7.343 × 10¹⁰¹(102-digit number)

73433449904253830306…01111827778561648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.343 × 10¹⁰¹(102-digit number)

73433449904253830306…01111827778561648641

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