Block #287,659

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 10:11:45 AM · Difficulty 9.9869 · 6,507,774 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58448cdb14481a61b9d8aa8abec29cc57f8956579aa6b489f66f87375c75fb9c

View on Chainz ↗

Height

#287,659

Difficulty

9.986902

Transactions

Size

1.04 KB

Version

Bits

09fca599

Nonce

55,343

Timestamp

12/1/2013, 10:11:45 AM

Confirmations

6,507,774

Mined by

⛏️ caR0AKde1i4dpqpgDtEArAY3oRXX8K88R1bw6g

Merkle Root

1d40ede9294298c11c5122bee30c4a8ae5d0743d62207a718244756921882e02

Transactions (2)

Coinbaseb0e7d79fb54a73…281f2a876f8d10

1 in → 3 out10.0092 XPM165 B

AKde1i4d…88R1bw6g ASXEwJrb…E3MLWChF AYrgZtF4…6oLCC7XK

a666646c1f98fc…74c7ff549e0f51

5 in → 2 out60.5814 XPM818 B

Ad3EHKGw…B9bpLhio AJcu1Ark…MKZhNEmD

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.

1.226 × 10⁸⁸(89-digit number)

12268985120385853343…27638548964240559199

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

1.226 × 10⁸⁸(89-digit number)

12268985120385853343…27638548964240559199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.226 × 10⁸⁸(89-digit number)

12268985120385853343…27638548964240559201

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

2.453 × 10⁸⁸(89-digit number)

24537970240771706687…55277097928481118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.453 × 10⁸⁸(89-digit number)

24537970240771706687…55277097928481118401

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

4.907 × 10⁸⁸(89-digit number)

49075940481543413374…10554195856962236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.907 × 10⁸⁸(89-digit number)

49075940481543413374…10554195856962236801

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

9.815 × 10⁸⁸(89-digit number)

98151880963086826749…21108391713924473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.815 × 10⁸⁸(89-digit number)

98151880963086826749…21108391713924473601

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

1.963 × 10⁸⁹(90-digit number)

19630376192617365349…42216783427848947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.963 × 10⁸⁹(90-digit number)

19630376192617365349…42216783427848947201

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