Block #422,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 12:40:25 AM · Difficulty 10.3653 · 6,375,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad3447c7b8d317eba93b61583c388af63a501b6c8b421cec61bbdf5f5ca13451

View on Chainz ↗

Height

#422,753

Difficulty

10.365334

Transactions

Size

2.53 KB

Version

Bits

0a5d8680

Nonce

16,756

Timestamp

2/28/2014, 12:40:25 AM

Confirmations

6,375,368

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

87b2cd2431f2458da6b38de2cf9ec13667776a721f19348d9f6f1459b64e629d

Transactions (5)

Coinbasea31b12033cb088…d67cb68e326027

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

04aafd74d98247…d2f704f0d5a456

6 in → 2 out6.0193 XPM964 B

AJckuMU8…huGaDZvc AWngTdRJ…2geutj4n

79093a771f569f…acd0f314bba2e9

6 in → 2 out6.0907 XPM967 B

AJckuMU8…huGaDZvc AdvqPLCg…ERkRNZjf

a73bb0e319295f…15b5245fdb4ffb

1 in → 2 out6.2673 XPM227 B

APfegr1C…RnjWv4aJ AXNVLKpH…GHdwoAxs

a0522ab36751e9…873e1c8db04444

1 in → 2 out4.4545 XPM226 B

ATGRJgXo…JhttfbDf AZf4XWkX…Lfz4oE4Q

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.

5.461 × 10¹⁰⁶(107-digit number)

54613029081789133113…79493512961995217919

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

5.461 × 10¹⁰⁶(107-digit number)

54613029081789133113…79493512961995217919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.461 × 10¹⁰⁶(107-digit number)

54613029081789133113…79493512961995217921

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

1.092 × 10¹⁰⁷(108-digit number)

10922605816357826622…58987025923990435839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.092 × 10¹⁰⁷(108-digit number)

10922605816357826622…58987025923990435841

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

2.184 × 10¹⁰⁷(108-digit number)

21845211632715653245…17974051847980871679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.184 × 10¹⁰⁷(108-digit number)

21845211632715653245…17974051847980871681

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

4.369 × 10¹⁰⁷(108-digit number)

43690423265431306490…35948103695961743359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.369 × 10¹⁰⁷(108-digit number)

43690423265431306490…35948103695961743361

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

8.738 × 10¹⁰⁷(108-digit number)

87380846530862612981…71896207391923486719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.738 × 10¹⁰⁷(108-digit number)

87380846530862612981…71896207391923486721

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