Block #1,544,407

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2016, 8:09:47 PM · Difficulty 10.6523 · 5,266,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bf44bd83d7d4dda44decef54a53e3a944b1a6aa61129b80d2e2bf8aeaf84c72

View on Chainz ↗

Height

#1,544,407

Difficulty

10.652259

Transactions

Size

3.16 KB

Version

Bits

0aa6fa6f

Nonce

1,278,347,373

Timestamp

4/16/2016, 8:09:47 PM

Confirmations

5,266,667

Mined by

⛏️ P2SHAUWCLgi2t4Yc2nzQTps6KacqpFMhCo6KKP

Merkle Root

d4f843e19e399831284d21201ccf9be6b42b301fa0b33809f06a1fabe1b29ca3

Transactions (2)

Coinbase903acde80fc6f2…4e499f4150a055

1 in → 1 out8.8400 XPM109 B

AUWCLgi2…MhCo6KKP

c4be079bea6eff…99a0c01830ac3a

20 in → 2 out80.3800 XPM2.96 KB

ATB74oXY…stL4TZyf ALb9t1Dg…adW55uRA

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.

5.757 × 10⁹¹(92-digit number)

57579826738266382036…84332326692764864019

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

5.757 × 10⁹¹(92-digit number)

57579826738266382036…84332326692764864019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.757 × 10⁹¹(92-digit number)

57579826738266382036…84332326692764864021

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

1.151 × 10⁹²(93-digit number)

11515965347653276407…68664653385529728039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.151 × 10⁹²(93-digit number)

11515965347653276407…68664653385529728041

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

2.303 × 10⁹²(93-digit number)

23031930695306552814…37329306771059456079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.303 × 10⁹²(93-digit number)

23031930695306552814…37329306771059456081

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

4.606 × 10⁹²(93-digit number)

46063861390613105629…74658613542118912159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.606 × 10⁹²(93-digit number)

46063861390613105629…74658613542118912161

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

9.212 × 10⁹²(93-digit number)

92127722781226211258…49317227084237824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.212 × 10⁹²(93-digit number)

92127722781226211258…49317227084237824321

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 #1,544,407

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