Block #703,945

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2014, 10:07:32 AM · Difficulty 10.9591 · 6,122,489 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

857be909425b298dde6d756d50cb0e04624b9334ec7527d14abbcc3b12992a6c

View on Chainz ↗

Height

#703,945

Difficulty

10.959083

Transactions

Size

1.41 KB

Version

Bits

0af58670

Nonce

654,608,891

Timestamp

9/2/2014, 10:07:32 AM

Confirmations

6,122,489

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c13bcf71c13c940a8965a96386a2e0aa4f6ecafaabbd5c6660d8c92d6930a09c

Transactions (5)

Coinbasec1b400ce504d64…ffc20b8323e5a5

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

a3eac07d99ba13…c8e248065db81b

2 in → 2 out14.8899 XPM374 B

AdouUT3o…oqYnLrrA ASMoy1y2…61cfmZPb

e6133cc07ba547…4443dfc161db78

1 in → 3 out6.0835 XPM259 B

AGqSWjWQ…gzSSkRFQ AeKNrjNj…1NEq95Ta AUfa5LFJ…C4BhhWGa

cce429a5e5855f…052e4e6b1568eb

1 in → 2 out5.0823 XPM227 B

AKPN3QNR…2VrMQnQC AYrwBKyU…1S6w2wRP

cc19dd1aad9a77…d9b11e94d5caf8

2 in → 2 out1.4600 XPM373 B

APFJWTjC…qUVR7HhS Abu213sj…RaQgm7VL

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.

1.569 × 10⁹⁴(95-digit number)

15695228948710920401…16262946942069599759

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

1.569 × 10⁹⁴(95-digit number)

15695228948710920401…16262946942069599759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.569 × 10⁹⁴(95-digit number)

15695228948710920401…16262946942069599761

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

3.139 × 10⁹⁴(95-digit number)

31390457897421840803…32525893884139199519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.139 × 10⁹⁴(95-digit number)

31390457897421840803…32525893884139199521

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

6.278 × 10⁹⁴(95-digit number)

62780915794843681606…65051787768278399039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.278 × 10⁹⁴(95-digit number)

62780915794843681606…65051787768278399041

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

1.255 × 10⁹⁵(96-digit number)

12556183158968736321…30103575536556798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.255 × 10⁹⁵(96-digit number)

12556183158968736321…30103575536556798081

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

2.511 × 10⁹⁵(96-digit number)

25112366317937472642…60207151073113596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.511 × 10⁹⁵(96-digit number)

25112366317937472642…60207151073113596161

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 #703,945

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