Block #1,389,543

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2015, 2:10:39 AM · Difficulty 10.8105 · 5,435,495 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12419c2001362080e84e4514a2152fbae76c5315df6757edecc186f031241fd3

View on Chainz ↗

Height

#1,389,543

Difficulty

10.810537

Transactions

Size

800 B

Version

Bits

0acf7f5c

Nonce

1,703,578,697

Timestamp

12/29/2015, 2:10:39 AM

Confirmations

5,435,495

Mined by

⛏️ P2SHALZMCaQp6fLSfqq4h2BotvbUiz61tvcvhH

Merkle Root

fea56ca7fb6c23d7463ee53e952fc95c65af2230654a2eb4e12ceae22e1860bf

Transactions (2)

Coinbase1dac41e9662c7e…ffae7feb03b5ff

1 in → 1 out8.5500 XPM110 B

ALZMCaQp…61tvcvhH

75036b2254ebef…2be4b21582a2cf

1 in → 13 out89.3127 XPM600 B

AJhtMLRr…zMcSLotL AReGKD9t…iGYSRrKZ ATUW1u6X…YYAQqaKM AbpVdxCi…pPEhfykH AKu3reXg…YJfjCxij

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.

1.556 × 10⁹⁵(96-digit number)

15566075030303751444…60851157826311064319

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

1.556 × 10⁹⁵(96-digit number)

15566075030303751444…60851157826311064319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.556 × 10⁹⁵(96-digit number)

15566075030303751444…60851157826311064321

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

3.113 × 10⁹⁵(96-digit number)

31132150060607502889…21702315652622128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.113 × 10⁹⁵(96-digit number)

31132150060607502889…21702315652622128641

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

6.226 × 10⁹⁵(96-digit number)

62264300121215005778…43404631305244257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.226 × 10⁹⁵(96-digit number)

62264300121215005778…43404631305244257281

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

1.245 × 10⁹⁶(97-digit number)

12452860024243001155…86809262610488514559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.245 × 10⁹⁶(97-digit number)

12452860024243001155…86809262610488514561

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

2.490 × 10⁹⁶(97-digit number)

24905720048486002311…73618525220977029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.490 × 10⁹⁶(97-digit number)

24905720048486002311…73618525220977029121

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 #1,389,543

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