Block #1,458,551

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/15/2016, 7:03:39 PM · Difficulty 10.7658 · 5,385,275 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a581911fce1a9a7787ad45c4339bea1b2a63e714c94650be48935e441b949172

View on Chainz ↗

Height

#1,458,551

Difficulty

10.765802

Transactions

Size

1.08 KB

Version

Bits

0ac40b96

Nonce

339,837,604

Timestamp

2/15/2016, 7:03:39 PM

Confirmations

5,385,275

Mined by

⛏️ P2SHAbvyrsvWeH2q6acwGss1sHoRjqVvqGpkq6

Merkle Root

2bd49e1e943f75be97308becf888e49528e8308e0e0ccbc3b0251c33e3970d44

Transactions (2)

Coinbase8c54e94c1c2c93…ecc4a170c5ddfd

1 in → 1 out8.6200 XPM110 B

AbvyrsvW…VvqGpkq6

8b3ca98a3cd5a2…92cfd0415d1b53

1 in → 22 out27.6109 XPM905 B

Ae3mvu1y…WJjV3Hsc AZqU9K1n…q9nSDZkU Ac9q4y8s…BuiSzVFd ALPnuhwt…Lzmzt42z AWL2maao…gT97jevq

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.

1.742 × 10⁹⁷(98-digit number)

17424434103462074461…21853049231263416319

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

1.742 × 10⁹⁷(98-digit number)

17424434103462074461…21853049231263416319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.742 × 10⁹⁷(98-digit number)

17424434103462074461…21853049231263416321

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

3.484 × 10⁹⁷(98-digit number)

34848868206924148923…43706098462526832639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.484 × 10⁹⁷(98-digit number)

34848868206924148923…43706098462526832641

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

6.969 × 10⁹⁷(98-digit number)

69697736413848297847…87412196925053665279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.969 × 10⁹⁷(98-digit number)

69697736413848297847…87412196925053665281

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

1.393 × 10⁹⁸(99-digit number)

13939547282769659569…74824393850107330559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.393 × 10⁹⁸(99-digit number)

13939547282769659569…74824393850107330561

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

2.787 × 10⁹⁸(99-digit number)

27879094565539319139…49648787700214661119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.787 × 10⁹⁸(99-digit number)

27879094565539319139…49648787700214661121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.575 × 10⁹⁸(99-digit number)

55758189131078638278…99297575400429322239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,458,551

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