Block #718,603

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/13/2014, 9:15:31 AM · Difficulty 10.9494 · 6,085,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a761dcc53974e223a1824fdd4f596a5b54b7811e8b22403f37c11f3acca726c3

View on Chainz ↗

Height

#718,603

Difficulty

10.949402

Transactions

Size

415 B

Version

Bits

0af30c08

Nonce

160,774

Timestamp

9/13/2014, 9:15:31 AM

Confirmations

6,085,176

Mined by

⛏️ aTAYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

a85640b5dee1d0c918ba8d752a8cc2e5a3e4dd1a2581e5ba49c34ea2fd2ed990

Transactions (2)

Coinbasee38267fc4d9868…43f64172c0a59f

1 in → 1 out8.3300 XPM97 B

AYCeLhqB…eqGM6KK1

87e7cb5ef95248…1856e58eb878ab

1 in → 2 out6.7128 XPM226 B

ANZUxYNW…P1pZfYxg AccJ1iCU…3gdH4ioV

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.

2.342 × 10⁹⁹(100-digit number)

23420714496660636509…04934176335296785919

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

2.342 × 10⁹⁹(100-digit number)

23420714496660636509…04934176335296785919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.342 × 10⁹⁹(100-digit number)

23420714496660636509…04934176335296785921

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

4.684 × 10⁹⁹(100-digit number)

46841428993321273018…09868352670593571839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.684 × 10⁹⁹(100-digit number)

46841428993321273018…09868352670593571841

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

9.368 × 10⁹⁹(100-digit number)

93682857986642546036…19736705341187143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.368 × 10⁹⁹(100-digit number)

93682857986642546036…19736705341187143681

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

1.873 × 10¹⁰⁰(101-digit number)

18736571597328509207…39473410682374287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.873 × 10¹⁰⁰(101-digit number)

18736571597328509207…39473410682374287361

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

3.747 × 10¹⁰⁰(101-digit number)

37473143194657018414…78946821364748574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.747 × 10¹⁰⁰(101-digit number)

37473143194657018414…78946821364748574721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.494 × 10¹⁰⁰(101-digit number)

74946286389314036829…57893642729497149439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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