Block #1,415,109

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2016, 2:07:17 AM · Difficulty 10.7978 · 5,402,863 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59eca6176a35adbec27eb9b06ca7aed8d31401534310109a5e41a194f9e117c4

View on Chainz ↗

Height

#1,415,109

Difficulty

10.797829

Transactions

Size

836 B

Version

Bits

0acc3e84

Nonce

1,531,273,199

Timestamp

1/16/2016, 2:07:17 AM

Confirmations

5,402,863

Mined by

⛏️ P2SHAPsssnUGNa9j6Y21aDSGcKjvSGdj8xzA54

Merkle Root

3a3266f27eb575b8b07ca730cf7649a44172b4a2cd2bc828f02ba0688dc3c7f7

Transactions (2)

Coinbase1f22a8e7237e39…22b19b89769a6f

1 in → 1 out8.5700 XPM110 B

APsssnUG…dj8xzA54

83872f27706dde…ff6f98eb68fb1c

1 in → 14 out85.4762 XPM635 B

AGAZXoXz…ypRftL7n ASf56EmJ…urQdVeD5 ATyHFdjS…kku74cEm AMBNEUEi…CrcHny5p AZAb4toh…qfnaNScw

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.

2.720 × 10⁹⁷(98-digit number)

27201682735455627145…42778694409432063999

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

2.720 × 10⁹⁷(98-digit number)

27201682735455627145…42778694409432063999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.720 × 10⁹⁷(98-digit number)

27201682735455627145…42778694409432064001

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

5.440 × 10⁹⁷(98-digit number)

54403365470911254290…85557388818864127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.440 × 10⁹⁷(98-digit number)

54403365470911254290…85557388818864128001

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

1.088 × 10⁹⁸(99-digit number)

10880673094182250858…71114777637728255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.088 × 10⁹⁸(99-digit number)

10880673094182250858…71114777637728256001

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

2.176 × 10⁹⁸(99-digit number)

21761346188364501716…42229555275456511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.176 × 10⁹⁸(99-digit number)

21761346188364501716…42229555275456512001

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

4.352 × 10⁹⁸(99-digit number)

43522692376729003432…84459110550913023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.352 × 10⁹⁸(99-digit number)

43522692376729003432…84459110550913024001

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 #1,415,109

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