Block #1,350,165

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2015, 7:51:43 PM · Difficulty 10.8044 · 5,441,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5157a352235b6eca476683c5744a8fcc706c0fc96b185456d24684a16c4f6c89

View on Chainz ↗

Height

#1,350,165

Difficulty

10.804380

Transactions

Size

798 B

Version

Bits

0acdebd8

Nonce

1,064,332,551

Timestamp

12/1/2015, 7:51:43 PM

Confirmations

5,441,589

Merkle Root

1b0040a81340f7d3b99cba3932ce2193c570e75ac2a9705c725e6ce18818fcbc

Transactions (3)

Coinbase9eb1dec88657d8…d11867558cb349

1 in → 1 out8.5700 XPM109 B

AdycDWWU…5uLQ6XRY

98681161b741c2…9ffea9697aaf0d

2 in → 2 out11.4733 XPM374 B

AJRwGPSP…QDRWdi2B AdiVpEUg…5vXD9LYs

7e121a9d646b55…bcd700dfa89d7d

1 in → 2 out5.6956 XPM226 B

AcuM7XiJ…5uND8Jce AcDLVo3g…PKGaAVjp

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.

9.452 × 10⁹¹(92-digit number)

94525667597001117533…26743937160410621679

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

9.452 × 10⁹¹(92-digit number)

94525667597001117533…26743937160410621679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.452 × 10⁹¹(92-digit number)

94525667597001117533…26743937160410621681

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

1.890 × 10⁹²(93-digit number)

18905133519400223506…53487874320821243359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.890 × 10⁹²(93-digit number)

18905133519400223506…53487874320821243361

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

3.781 × 10⁹²(93-digit number)

37810267038800447013…06975748641642486719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.781 × 10⁹²(93-digit number)

37810267038800447013…06975748641642486721

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

7.562 × 10⁹²(93-digit number)

75620534077600894026…13951497283284973439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.562 × 10⁹²(93-digit number)

75620534077600894026…13951497283284973441

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

1.512 × 10⁹³(94-digit number)

15124106815520178805…27902994566569946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.512 × 10⁹³(94-digit number)

15124106815520178805…27902994566569946881

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