Block #859,406

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.

3.300 × 10⁹⁴(95-digit number)

33008865662952696742…26419113717677432139

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

3.300 × 10⁹⁴(95-digit number)

33008865662952696742…26419113717677432139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.300 × 10⁹⁴(95-digit number)

33008865662952696742…26419113717677432141

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

6.601 × 10⁹⁴(95-digit number)

66017731325905393485…52838227435354864279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.601 × 10⁹⁴(95-digit number)

66017731325905393485…52838227435354864281

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

1.320 × 10⁹⁵(96-digit number)

13203546265181078697…05676454870709728559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.320 × 10⁹⁵(96-digit number)

13203546265181078697…05676454870709728561

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

2.640 × 10⁹⁵(96-digit number)

26407092530362157394…11352909741419457119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.640 × 10⁹⁵(96-digit number)

26407092530362157394…11352909741419457121

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

5.281 × 10⁹⁵(96-digit number)

52814185060724314788…22705819482838914239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.281 × 10⁹⁵(96-digit number)

52814185060724314788…22705819482838914241

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

1.056 × 10⁹⁶(97-digit number)

10562837012144862957…45411638965677828479

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 #859,406

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