Block #461,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 11:42:51 AM · Difficulty 10.4152 · 6,344,612 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d69e7c25e6319adcc53279209750b180a56d0393114970a5ffe94917ced0af33

View on Chainz ↗

Height

#461,083

Difficulty

10.415219

Transactions

Size

403 B

Version

Bits

0a6a4bc5

Nonce

16,781,625

Timestamp

3/26/2014, 11:42:51 AM

Confirmations

6,344,612

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8a9aefb10d87fa5a35429ea2a398f11f4aa6a3a2d6eedef5867ed0ce13b077f7

Transactions (2)

Coinbasebfc8a162ce0fe7…21333d5b835899

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

1854d5a8c77a27…fbed7ded0cca39

1 in → 1 out3.3804 XPM192 B

AJpXdJ2o…TnRUu62Y

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.

2.413 × 10¹⁰⁶(107-digit number)

24131511875236950030…87612435780587162169

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

2.413 × 10¹⁰⁶(107-digit number)

24131511875236950030…87612435780587162169

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.413 × 10¹⁰⁶(107-digit number)

24131511875236950030…87612435780587162171

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

4.826 × 10¹⁰⁶(107-digit number)

48263023750473900060…75224871561174324339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.826 × 10¹⁰⁶(107-digit number)

48263023750473900060…75224871561174324341

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

9.652 × 10¹⁰⁶(107-digit number)

96526047500947800121…50449743122348648679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.652 × 10¹⁰⁶(107-digit number)

96526047500947800121…50449743122348648681

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

1.930 × 10¹⁰⁷(108-digit number)

19305209500189560024…00899486244697297359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.930 × 10¹⁰⁷(108-digit number)

19305209500189560024…00899486244697297361

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

3.861 × 10¹⁰⁷(108-digit number)

38610419000379120048…01798972489394594719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.861 × 10¹⁰⁷(108-digit number)

38610419000379120048…01798972489394594721

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