Block #1,071,870

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2015, 6:52:18 AM · Difficulty 10.7419 · 5,736,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3d85228b2753c44c27504a847ed6a8754e4cc41dccdbac2954fade5ba03d7c3

View on Chainz ↗

Height

#1,071,870

Difficulty

10.741924

Transactions

Size

37.86 KB

Version

Bits

0abdeebf

Nonce

2,318,224,165

Timestamp

5/23/2015, 6:52:18 AM

Confirmations

5,736,058

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0b883099767fa11805d08bd1c392076359a85f184f85847d2fda1b2cd6882f0b

Transactions (2)

Coinbase8240c2b86f9d6e…42eaa59ea51710

1 in → 1 out9.0400 XPM116 B

ANSXnLY2…Sd25TjkD

f483b399f2e224…af3242572175bb

260 in → 2 out2950.2927 XPM37.66 KB

ARjHFrvg…BQzkuW1E AHh8tQMB…yLrV7rQm

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.

2.787 × 10⁹⁵(96-digit number)

27877102670471108211…86573224732777849619

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

2.787 × 10⁹⁵(96-digit number)

27877102670471108211…86573224732777849619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.787 × 10⁹⁵(96-digit number)

27877102670471108211…86573224732777849621

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

5.575 × 10⁹⁵(96-digit number)

55754205340942216423…73146449465555699239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.575 × 10⁹⁵(96-digit number)

55754205340942216423…73146449465555699241

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

1.115 × 10⁹⁶(97-digit number)

11150841068188443284…46292898931111398479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁶(97-digit number)

11150841068188443284…46292898931111398481

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

2.230 × 10⁹⁶(97-digit number)

22301682136376886569…92585797862222796959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.230 × 10⁹⁶(97-digit number)

22301682136376886569…92585797862222796961

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

4.460 × 10⁹⁶(97-digit number)

44603364272753773138…85171595724445593919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.460 × 10⁹⁶(97-digit number)

44603364272753773138…85171595724445593921

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 #1,071,870

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