Block #286,949

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 2:51:20 AM · Difficulty 9.9862 · 6,537,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45d33905dbca7434952564e9dc4f2756a15f4d995f3ecf731578655e05670d21

View on Chainz ↗

Height

#286,949

Difficulty

9.986158

Transactions

Size

1.18 KB

Version

Bits

09fc74dc

Nonce

190,526

Timestamp

12/1/2013, 2:51:20 AM

Confirmations

6,537,651

Mined by

⛏️ `aRAKEwr54iEsuosjdBu66r2F564f9BfmMkRh

Merkle Root

eab90a1a26baf0a163edf07b10516b16635be90f472130563b2b9c851e339a1c

Transactions (1)

Coinbaseeab90a1a26baf0…2b9c851e339a1c

1 in → 31 out9.9900 XPM1.09 KB

AKEwr54i…9BfmMkRh AHfwsMTb…pY1MpjeT AYcLTeXR…bscgPops Aca5eCkn…5cumQ9Pt AJ3bhpLE…wUY61F8E

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.

7.921 × 10⁹⁴(95-digit number)

79218325756177037807…78933192370881331199

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

7.921 × 10⁹⁴(95-digit number)

79218325756177037807…78933192370881331199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.921 × 10⁹⁴(95-digit number)

79218325756177037807…78933192370881331201

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

1.584 × 10⁹⁵(96-digit number)

15843665151235407561…57866384741762662399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.584 × 10⁹⁵(96-digit number)

15843665151235407561…57866384741762662401

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

3.168 × 10⁹⁵(96-digit number)

31687330302470815123…15732769483525324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.168 × 10⁹⁵(96-digit number)

31687330302470815123…15732769483525324801

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

6.337 × 10⁹⁵(96-digit number)

63374660604941630246…31465538967050649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.337 × 10⁹⁵(96-digit number)

63374660604941630246…31465538967050649601

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

1.267 × 10⁹⁶(97-digit number)

12674932120988326049…62931077934101299199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #286,949

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