Block #1,597,139

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2016, 9:05:56 PM · Difficulty 10.6106 · 5,243,509 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e49249a6619fa06bbeed957fd01eddf83717242689a63b72dbbee139652950fa

View on Chainz ↗

Height

#1,597,139

Difficulty

10.610610

Transactions

Size

1.25 KB

Version

Bits

0a9c50ed

Nonce

746,469,348

Timestamp

5/23/2016, 9:05:56 PM

Confirmations

5,243,509

Mined by

⛏️ P2SHASQ5R3gbdw9By7jkuFQ3dWnNoJumTTq3kx

Merkle Root

c0ee65ead1f59c2e9843b1f19c8928bb4f8e5cd149ec4ae9e7acfbf5e3bf0048

Transactions (2)

Coinbase8e6a00e0c97d95…b4830d6e0adfda

1 in → 1 out8.8900 XPM109 B

ASQ5R3gb…umTTq3kx

ded11d9c496f96…3d98c2773dcbf9

1 in → 27 out28.2983 XPM1.05 KB

AQ3AedN2…x7WUWXmQ AZUi8isZ…PEXp78xK AZ5HksWX…jBomsELm AagSoUwK…WPXS9dK2 AZxYgUyu…gXvnhrhn

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.

9.554 × 10⁹³(94-digit number)

95546406390574942759…83776642930029075359

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

9.554 × 10⁹³(94-digit number)

95546406390574942759…83776642930029075359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.554 × 10⁹³(94-digit number)

95546406390574942759…83776642930029075361

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

1.910 × 10⁹⁴(95-digit number)

19109281278114988551…67553285860058150719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.910 × 10⁹⁴(95-digit number)

19109281278114988551…67553285860058150721

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

3.821 × 10⁹⁴(95-digit number)

38218562556229977103…35106571720116301439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.821 × 10⁹⁴(95-digit number)

38218562556229977103…35106571720116301441

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

7.643 × 10⁹⁴(95-digit number)

76437125112459954207…70213143440232602879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.643 × 10⁹⁴(95-digit number)

76437125112459954207…70213143440232602881

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

1.528 × 10⁹⁵(96-digit number)

15287425022491990841…40426286880465205759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.528 × 10⁹⁵(96-digit number)

15287425022491990841…40426286880465205761

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 #1,597,139

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