Block #463,776

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 8:55:32 AM · Difficulty 10.4140 · 6,344,397 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

661e2dbe8e26af4c85e53e1d31410db6e99ed665a00216d615fe3729a1bf501f

View on Chainz ↗

Height

#463,776

Difficulty

10.414043

Transactions

Size

5.26 KB

Version

Bits

0a69feb5

Nonce

9,308

Timestamp

3/28/2014, 8:55:32 AM

Confirmations

6,344,397

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a7681682b45d83a99461703d2c5e8e7c7d2d23ac1ae0d895950eeb54d5906cd8

Transactions (3)

Coinbase9e43062f4a8a36…278e2531eb99c5

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

ed2d0f0c108a99…97bc2882b7599a

15 in → 61 out130.7948 XPM4.20 KB

AKETzsmH…Z9z4oYx7 Af1Eejkx…cKmYn3YE APQCLq5D…cpNbYpoy AUkdqaxr…4jcbMUQ7 AcKeq82d…Ym6LNchU

e2f48a5d1bae19…07a39719368f25

4 in → 12 out36.8100 XPM873 B

ALLRNz7D…1vRxMn8t AeKNrjNj…1NEq95Ta AYpANtX5…cpBRh2BL ATz1Sryu…PWZHWKYx AK6jxxMy…1dDKDr5h

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.

1.275 × 10¹⁰¹(102-digit number)

12758475648845661443…65369510627277414399

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

1.275 × 10¹⁰¹(102-digit number)

12758475648845661443…65369510627277414399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10¹⁰¹(102-digit number)

12758475648845661443…65369510627277414401

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

2.551 × 10¹⁰¹(102-digit number)

25516951297691322887…30739021254554828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.551 × 10¹⁰¹(102-digit number)

25516951297691322887…30739021254554828801

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

5.103 × 10¹⁰¹(102-digit number)

51033902595382645775…61478042509109657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.103 × 10¹⁰¹(102-digit number)

51033902595382645775…61478042509109657601

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

1.020 × 10¹⁰²(103-digit number)

10206780519076529155…22956085018219315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10¹⁰²(103-digit number)

10206780519076529155…22956085018219315201

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

2.041 × 10¹⁰²(103-digit number)

20413561038153058310…45912170036438630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.041 × 10¹⁰²(103-digit number)

20413561038153058310…45912170036438630401

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 #463,776

Cookie Preferences