Block #456,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 2:54:09 AM · Difficulty 10.4166 · 6,352,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f07ccbb101f57a7a4cd9d2571389731d543cc200aee7cf8d52c62b9261e93ab8

View on Chainz ↗

Height

#456,274

Difficulty

10.416587

Transactions

Size

1.27 KB

Version

Bits

0a6aa56a

Nonce

224,765

Timestamp

3/23/2014, 2:54:09 AM

Confirmations

6,352,952

Mined by

⛏️ Rh:uAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

991500fb4189c56af9b9a9573b6e6a4a55b00706f921f9c129ed64837cbdcea2

Transactions (2)

Coinbase33d1aa6f80a1f5…435590575d16ac

1 in → 23 out9.2100 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw APtc8nU2…tp6qFHwW AH5mD99t…Spv1yg4N ATp4jJhs…TbSgR8Qb

dded029337dff8…adaa1ed231c303

1 in → 6 out13.9567 XPM362 B

AR7sWeJE…4CzZHz73 AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ

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.

8.196 × 10¹⁰⁰(101-digit number)

81966426102916217571…58887169909172259839

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

8.196 × 10¹⁰⁰(101-digit number)

81966426102916217571…58887169909172259839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.196 × 10¹⁰⁰(101-digit number)

81966426102916217571…58887169909172259841

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

1.639 × 10¹⁰¹(102-digit number)

16393285220583243514…17774339818344519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.639 × 10¹⁰¹(102-digit number)

16393285220583243514…17774339818344519681

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

3.278 × 10¹⁰¹(102-digit number)

32786570441166487028…35548679636689039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.278 × 10¹⁰¹(102-digit number)

32786570441166487028…35548679636689039361

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

6.557 × 10¹⁰¹(102-digit number)

65573140882332974057…71097359273378078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.557 × 10¹⁰¹(102-digit number)

65573140882332974057…71097359273378078721

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

1.311 × 10¹⁰²(103-digit number)

13114628176466594811…42194718546756157439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.311 × 10¹⁰²(103-digit number)

13114628176466594811…42194718546756157441

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 #456,274

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