Block #704,002

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2014, 11:06:00 AM · Difficulty 10.9591 · 6,099,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

270d1a1daac6054e8b389bce3b45e179cdbf5398a26e8265fa889bb35982d7fa

View on Chainz ↗

Height

#704,002

Difficulty

10.959054

Transactions

Size

658 B

Version

Bits

0af58495

Nonce

652,828,743

Timestamp

9/2/2014, 11:06:00 AM

Confirmations

6,099,348

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

56deac38619c5c2e6032c112e3478feafb2362f4f4e5ad9fc745453bd910e4f0

Transactions (3)

Coinbase91a3dc5a89fd7c…4e42cabb90c8a7

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

6f440f7f6262be…627935b04c4352

1 in → 2 out8.3000 XPM192 B

AbFJHDk8…PBzZicHZ AK2bFEFr…d3Cd9Pdh

723cbb2dbd42f9…9379b405a1505e

1 in → 4 out8.3000 XPM260 B

AeKNrjNj…1NEq95Ta AKinBSz6…c5jHh6RZ AJcmFad4…YNAMFS3w AYk6SdQf…UGcYbb4t

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.

2.354 × 10⁹⁵(96-digit number)

23540947078968609797…36553608756026438199

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

2.354 × 10⁹⁵(96-digit number)

23540947078968609797…36553608756026438199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.354 × 10⁹⁵(96-digit number)

23540947078968609797…36553608756026438201

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

4.708 × 10⁹⁵(96-digit number)

47081894157937219595…73107217512052876399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.708 × 10⁹⁵(96-digit number)

47081894157937219595…73107217512052876401

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

9.416 × 10⁹⁵(96-digit number)

94163788315874439191…46214435024105752799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.416 × 10⁹⁵(96-digit number)

94163788315874439191…46214435024105752801

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

1.883 × 10⁹⁶(97-digit number)

18832757663174887838…92428870048211505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.883 × 10⁹⁶(97-digit number)

18832757663174887838…92428870048211505601

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

3.766 × 10⁹⁶(97-digit number)

37665515326349775676…84857740096423011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.766 × 10⁹⁶(97-digit number)

37665515326349775676…84857740096423011201

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