Block #1,597,302

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2016, 11:46:31 PM · Difficulty 10.6109 · 5,227,349 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fac602dafa6150af4d0b20332a64275e05fa0df654fbb44313465b1c19374112

View on Chainz ↗

Height

#1,597,302

Difficulty

10.610871

Transactions

Size

3.80 KB

Version

Bits

0a9c6208

Nonce

162,161,060

Timestamp

5/23/2016, 11:46:31 PM

Confirmations

5,227,349

Mined by

⛏️ P2SHAP7sG2oT8DwkXQDH59kWbBtcbvjicXCBeY

Merkle Root

9ad1e765a19124f179556643ca13ff1e19f8f108532d9f81f2352cc81e3b5738

Transactions (3)

Coinbasee536991e793ad9…f6a69099b4d21e

1 in → 1 out8.9200 XPM110 B

AP7sG2oT…jicXCBeY

66481175500339…9691023ab6b554

2 in → 51 out4.9879 XPM1.99 KB

AdvNP7qN…6vL7sa7x AZ3cZHxS…1qdoLqba AemPG26K…WxK2uVB4 ARwc14ci…MRUcBvQP AapqHFCy…2AdM5byX

45e1d78070fc3a…3b09d2d6c751f4

1 in → 44 out0.6708 XPM1.62 KB

AX5tjeiy…SQR4CaHH AYAFJks2…JLSZ87zS ALWcRwqS…KAy9F9nQ ARjqc3AM…6vtNb1sa ANK6vVVy…fq6sCpRH

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.

9.289 × 10⁹³(94-digit number)

92897561097665769948…11085872349647603439

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

9.289 × 10⁹³(94-digit number)

92897561097665769948…11085872349647603439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.289 × 10⁹³(94-digit number)

92897561097665769948…11085872349647603441

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

1.857 × 10⁹⁴(95-digit number)

18579512219533153989…22171744699295206879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.857 × 10⁹⁴(95-digit number)

18579512219533153989…22171744699295206881

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

3.715 × 10⁹⁴(95-digit number)

37159024439066307979…44343489398590413759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.715 × 10⁹⁴(95-digit number)

37159024439066307979…44343489398590413761

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

7.431 × 10⁹⁴(95-digit number)

74318048878132615958…88686978797180827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.431 × 10⁹⁴(95-digit number)

74318048878132615958…88686978797180827521

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

1.486 × 10⁹⁵(96-digit number)

14863609775626523191…77373957594361655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.486 × 10⁹⁵(96-digit number)

14863609775626523191…77373957594361655041

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 #1,597,302

Cookie Preferences