Block #687,205

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/22/2014, 5:38:32 AM · Difficulty 10.9530 · 6,127,094 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

720e0d2915839250d4e15f78c4cab52daaafcbc33ceedb1665e78ab2309dc725

View on Chainz ↗

Height

#687,205

Difficulty

10.953036

Transactions

Size

1.15 KB

Version

Bits

0af3fa26

Nonce

624,524,316

Timestamp

8/22/2014, 5:38:32 AM

Confirmations

6,127,094

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

01a4fc154d68dca9f4dc7380b3ccae71b0f4b0926903dda05b9569da1924ea29

Transactions (4)

Coinbase67a1ae622e02f4…eb767181205593

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

3dd72427d51844…e86c34ae9a0e75

1 in → 2 out8.2900 XPM225 B

AGLaXD21…WaV9DiQV APVdfbfH…1FUmTWCf

2d81bae069f9f6…0569cee94791d3

3 in → 2 out23.4273 XPM521 B

APZZjcPT…mEjtCRTo AeqcLjZz…hSPZn4qD

30d4de32cbfa68…7942d577521098

1 in → 2 out1.1586 XPM227 B

AJuYBvYm…sV4C8wM2 Ae7YXEyn…hnSYZsCr

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.

1.035 × 10⁹⁷(98-digit number)

10350082798986399701…49886618474287189119

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

1.035 × 10⁹⁷(98-digit number)

10350082798986399701…49886618474287189119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.035 × 10⁹⁷(98-digit number)

10350082798986399701…49886618474287189121

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

2.070 × 10⁹⁷(98-digit number)

20700165597972799403…99773236948574378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.070 × 10⁹⁷(98-digit number)

20700165597972799403…99773236948574378241

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

4.140 × 10⁹⁷(98-digit number)

41400331195945598806…99546473897148756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.140 × 10⁹⁷(98-digit number)

41400331195945598806…99546473897148756481

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

8.280 × 10⁹⁷(98-digit number)

82800662391891197612…99092947794297512959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.280 × 10⁹⁷(98-digit number)

82800662391891197612…99092947794297512961

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

1.656 × 10⁹⁸(99-digit number)

16560132478378239522…98185895588595025919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.656 × 10⁹⁸(99-digit number)

16560132478378239522…98185895588595025921

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 #687,205

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