Block #748,480

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.

1.981 × 10⁹⁴(95-digit number)

19815144087537861801…01488457603080101479

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

1.981 × 10⁹⁴(95-digit number)

19815144087537861801…01488457603080101479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.981 × 10⁹⁴(95-digit number)

19815144087537861801…01488457603080101481

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

3.963 × 10⁹⁴(95-digit number)

39630288175075723602…02976915206160202959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.963 × 10⁹⁴(95-digit number)

39630288175075723602…02976915206160202961

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

7.926 × 10⁹⁴(95-digit number)

79260576350151447205…05953830412320405919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.926 × 10⁹⁴(95-digit number)

79260576350151447205…05953830412320405921

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

1.585 × 10⁹⁵(96-digit number)

15852115270030289441…11907660824640811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.585 × 10⁹⁵(96-digit number)

15852115270030289441…11907660824640811841

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

3.170 × 10⁹⁵(96-digit number)

31704230540060578882…23815321649281623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.170 × 10⁹⁵(96-digit number)

31704230540060578882…23815321649281623681

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

6.340 × 10⁹⁵(96-digit number)

63408461080121157764…47630643298563247359

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 #748,480

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