Block #418,850

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 5:03:09 AM · Difficulty 10.3830 · 6,376,393 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

076367af4beaf344b496389fab4b9fcd18a29d33d250f8138c77a059b162f012

View on Chainz ↗

Height

#418,850

Difficulty

10.383007

Transactions

Size

1.58 KB

Version

Bits

0a620cc5

Nonce

195,722

Timestamp

2/25/2014, 5:03:09 AM

Confirmations

6,376,393

Mined by

⛏️ "daS#BAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

946af7f6ee28657628bbc7078038e77edd331f403871a1aa20536633d3473126

Transactions (4)

Coinbase615b0c32d57608…e8fdb0ff698a1b

1 in → 23 out9.2505 XPM845 B

AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AXz2kWvX…V5ZFCDBd AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

b7d22efb9ee42b…a6762807af1acf

1 in → 2 out9.1900 XPM226 B

APfEVRPm…J921DcLA AXvwfUYp…qcyo5kD2

2cd9d91e1ac750…b62cdb1c649d31

1 in → 2 out9.1900 XPM227 B

AXNVLKpH…GHdwoAxs AWgLpWys…2fkucFHq

e0f49433230e24…8f626dfc389c6b

1 in → 2 out8.1776 XPM225 B

AcP8jseU…hwvN422m AYJr1JwS…SYfcvjyJ

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.

9.812 × 10⁹⁵(96-digit number)

98126907796847439372…42422004137499948479

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

9.812 × 10⁹⁵(96-digit number)

98126907796847439372…42422004137499948479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.812 × 10⁹⁵(96-digit number)

98126907796847439372…42422004137499948481

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

1.962 × 10⁹⁶(97-digit number)

19625381559369487874…84844008274999896959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.962 × 10⁹⁶(97-digit number)

19625381559369487874…84844008274999896961

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

3.925 × 10⁹⁶(97-digit number)

39250763118738975748…69688016549999793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.925 × 10⁹⁶(97-digit number)

39250763118738975748…69688016549999793921

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

7.850 × 10⁹⁶(97-digit number)

78501526237477951497…39376033099999587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.850 × 10⁹⁶(97-digit number)

78501526237477951497…39376033099999587841

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

1.570 × 10⁹⁷(98-digit number)

15700305247495590299…78752066199999175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.570 × 10⁹⁷(98-digit number)

15700305247495590299…78752066199999175681

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