Block #511,631

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2014, 9:02:21 AM · Difficulty 10.8306 · 6,295,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89f6525427854398fd6a8e3a962ca9b468a4ec4d1f9934d580e99f8e5c1dfb16

View on Chainz ↗

Height

#511,631

Difficulty

10.830584

Transactions

Size

811 B

Version

Bits

0ad4a127

Nonce

11,328,227

Timestamp

4/26/2014, 9:02:21 AM

Confirmations

6,295,555

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

000651afba0a88c97b4f634b4575f5ed79642f017ef090dc0585c44cef24ce8e

Transactions (3)

Coinbased74e2527e1e442…8e9314419c46f4

1 in → 1 out8.5300 XPM116 B

AbwWkWZt…kawDhufa

c9b41112f8390b…859336f9688254

2 in → 2 out10.0521 XPM376 B

Ae6scbKS…gGVX2st2 AWjAVXLr…eibfZdt4

79688bd43763aa…981552d5e5ad5e

1 in → 2 out5.4455 XPM226 B

AGpDqEvm…tM8eVrjR AQGZcxZX…yqEoZriQ

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.

6.183 × 10¹⁰⁰(101-digit number)

61833798040924467574…53801009549306188799

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

6.183 × 10¹⁰⁰(101-digit number)

61833798040924467574…53801009549306188799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.183 × 10¹⁰⁰(101-digit number)

61833798040924467574…53801009549306188801

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

1.236 × 10¹⁰¹(102-digit number)

12366759608184893514…07602019098612377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.236 × 10¹⁰¹(102-digit number)

12366759608184893514…07602019098612377601

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

2.473 × 10¹⁰¹(102-digit number)

24733519216369787029…15204038197224755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.473 × 10¹⁰¹(102-digit number)

24733519216369787029…15204038197224755201

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

4.946 × 10¹⁰¹(102-digit number)

49467038432739574059…30408076394449510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.946 × 10¹⁰¹(102-digit number)

49467038432739574059…30408076394449510401

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

9.893 × 10¹⁰¹(102-digit number)

98934076865479148119…60816152788899020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.893 × 10¹⁰¹(102-digit number)

98934076865479148119…60816152788899020801

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 #511,631

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