Block #675,568

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/13/2014, 1:52:44 AM · Difficulty 10.9651 · 6,140,659 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

daf1d164660d35b7e5dd10472686fc368ec3d4f381f8e4c18fa4852aee5bc6ca

View on Chainz ↗

Height

#675,568

Difficulty

10.965129

Transactions

Size

2.01 KB

Version

Bits

0af712b4

Nonce

2,065,240,417

Timestamp

8/13/2014, 1:52:44 AM

Confirmations

6,140,659

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

58698010b0311a28adffe83259c21bd8f7ee9679e31c8931376fe15397916268

Transactions (2)

Coinbase5d124c2ebf332b…d57f7b6998aff1

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

05da05a19d0cb5…8612a15f7a8934

12 in → 2 out20.1513 XPM1.81 KB

ANYfBTow…KbndYZWh AcaBJDt7…qFCSohbu

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.

2.647 × 10⁹⁸(99-digit number)

26470563199562907815…33473133598550261759

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

2.647 × 10⁹⁸(99-digit number)

26470563199562907815…33473133598550261759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.647 × 10⁹⁸(99-digit number)

26470563199562907815…33473133598550261761

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

5.294 × 10⁹⁸(99-digit number)

52941126399125815630…66946267197100523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.294 × 10⁹⁸(99-digit number)

52941126399125815630…66946267197100523521

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

1.058 × 10⁹⁹(100-digit number)

10588225279825163126…33892534394201047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.058 × 10⁹⁹(100-digit number)

10588225279825163126…33892534394201047041

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

2.117 × 10⁹⁹(100-digit number)

21176450559650326252…67785068788402094079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.117 × 10⁹⁹(100-digit number)

21176450559650326252…67785068788402094081

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

4.235 × 10⁹⁹(100-digit number)

42352901119300652504…35570137576804188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.235 × 10⁹⁹(100-digit number)

42352901119300652504…35570137576804188161

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 #675,568

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