Block #439,191

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 12:33:37 PM · Difficulty 10.3597 · 6,360,140 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89a7eff2b373eda5ff4edad4532b260a8a8d3c251524fe7b743a1b99ff8e9dc8

View on Chainz ↗

Height

#439,191

Difficulty

10.359691

Transactions

Size

1.62 KB

Version

Bits

0a5c14bb

Nonce

218,779

Timestamp

3/11/2014, 12:33:37 PM

Confirmations

6,360,140

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1280eef4bec55c5d5e31568f5ab2a134db8e24e570e9071822065562a69b7d88

Transactions (4)

Coinbase67a2be5c33d5ca…1da4d50e529fe5

1 in → 20 out9.3300 XPM743 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AcgDwGo8…BBFwbjVo AUFKXvnz…342ApNcm AXCBfU18…vZFjKTCm

25a40461a5099a…592b170c381b45

2 in → 2 out10.0206 XPM372 B

APaSkzEP…e9f176Qr ARW2ST2b…KfbxSQWE

9f96c4c7a9abc5…dc507631481a1a

1 in → 2 out5.1699 XPM226 B

AP4gNmAy…DqB1pDvn AcenZgci…dgEsobem

7ae431cd7e4393…93cd53641bc7e8

1 in → 2 out4.5534 XPM227 B

AXSuZm7K…JNBpTs3M AUpDUKSw…7JyxnNuz

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.

1.408 × 10¹⁰³(104-digit number)

14082621855167730307…64231616468255210239

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

1.408 × 10¹⁰³(104-digit number)

14082621855167730307…64231616468255210239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.408 × 10¹⁰³(104-digit number)

14082621855167730307…64231616468255210241

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

2.816 × 10¹⁰³(104-digit number)

28165243710335460614…28463232936510420479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.816 × 10¹⁰³(104-digit number)

28165243710335460614…28463232936510420481

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

5.633 × 10¹⁰³(104-digit number)

56330487420670921228…56926465873020840959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.633 × 10¹⁰³(104-digit number)

56330487420670921228…56926465873020840961

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

1.126 × 10¹⁰⁴(105-digit number)

11266097484134184245…13852931746041681919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.126 × 10¹⁰⁴(105-digit number)

11266097484134184245…13852931746041681921

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

2.253 × 10¹⁰⁴(105-digit number)

22532194968268368491…27705863492083363839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.253 × 10¹⁰⁴(105-digit number)

22532194968268368491…27705863492083363841

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