Block #1,072,568

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2015, 7:09:17 PM · Difficulty 10.7398 · 5,731,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40ae0c6a83f3cd2d54e847d21c7dca9cb2d58483076cba19688a940852c17187

View on Chainz ↗

Height

#1,072,568

Difficulty

10.739841

Transactions

Size

584 B

Version

Bits

0abd6634

Nonce

436,339,409

Timestamp

5/23/2015, 7:09:17 PM

Confirmations

5,731,099

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a3adeaf71e23c7390713a7f01c87420eb73c6fb6b37fbc1badfdf16b6fcea645

Transactions (2)

Coinbased7a35920a06e10…e0343380fee9ed

1 in → 1 out8.6700 XPM116 B

ANSXnLY2…Sd25TjkD

92e5fc2e60c7ce…fdacca17d7d7f5

2 in → 2 out1.2203 XPM376 B

Ab7Vamnz…tEmPcbG7 AHmcchxr…vBbydp5n

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.

1.760 × 10⁹⁹(100-digit number)

17604569900033886565…67538358327099064319

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

1.760 × 10⁹⁹(100-digit number)

17604569900033886565…67538358327099064319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.760 × 10⁹⁹(100-digit number)

17604569900033886565…67538358327099064321

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

3.520 × 10⁹⁹(100-digit number)

35209139800067773130…35076716654198128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.520 × 10⁹⁹(100-digit number)

35209139800067773130…35076716654198128641

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

7.041 × 10⁹⁹(100-digit number)

70418279600135546261…70153433308396257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.041 × 10⁹⁹(100-digit number)

70418279600135546261…70153433308396257281

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

1.408 × 10¹⁰⁰(101-digit number)

14083655920027109252…40306866616792514559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.408 × 10¹⁰⁰(101-digit number)

14083655920027109252…40306866616792514561

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

2.816 × 10¹⁰⁰(101-digit number)

28167311840054218504…80613733233585029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.816 × 10¹⁰⁰(101-digit number)

28167311840054218504…80613733233585029121

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