Block #2,873,924

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.

1.751 × 10⁹⁹(100-digit number)

17511954376658618137…59904170563076095999

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

1.751 × 10⁹⁹(100-digit number)

17511954376658618137…59904170563076095999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.751 × 10⁹⁹(100-digit number)

17511954376658618137…59904170563076096001

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

3.502 × 10⁹⁹(100-digit number)

35023908753317236275…19808341126152191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.502 × 10⁹⁹(100-digit number)

35023908753317236275…19808341126152192001

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

7.004 × 10⁹⁹(100-digit number)

70047817506634472550…39616682252304383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.004 × 10⁹⁹(100-digit number)

70047817506634472550…39616682252304384001

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

1.400 × 10¹⁰⁰(101-digit number)

14009563501326894510…79233364504608767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.400 × 10¹⁰⁰(101-digit number)

14009563501326894510…79233364504608768001

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

2.801 × 10¹⁰⁰(101-digit number)

28019127002653789020…58466729009217535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.801 × 10¹⁰⁰(101-digit number)

28019127002653789020…58466729009217536001

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

5.603 × 10¹⁰⁰(101-digit number)

56038254005307578040…16933458018435071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

5.603 × 10¹⁰⁰(101-digit number)

56038254005307578040…16933458018435072001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,873,924

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