Block #2,262,367

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/22/2017, 1:12:02 AM · Difficulty 10.9522 · 4,580,218 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d04aa0ac48c87937a2463e42397dc071e58844d8b84a3c09ba795bb1778d947

View on Chainz ↗

Height

#2,262,367

Difficulty

10.952155

Transactions

Size

426 B

Version

Bits

0af3c06f

Nonce

1,439,150,427

Timestamp

8/22/2017, 1:12:02 AM

Confirmations

4,580,218

Mined by

⛏️ P2SHAaUXHjEmaDyY4Lv5ZsC78BFGnybAjnxoSV

Merkle Root

33fa8ef316c14b8ecae877911f88cd135b3e8e99818ceb6c415f02b9746bfd50

Transactions (2)

Coinbase888158791662b1…6ccddd0ba6144f

1 in → 1 out8.3300 XPM110 B

AaUXHjEm…bAjnxoSV

fdb2a31c4f8377…e8ad23fcf34b58

1 in → 2 out120296.4797 XPM226 B

AUn2Kwfi…R8KZwnsu ASBTfoPT…gaa5DYhj

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.

1.224 × 10⁹⁵(96-digit number)

12240364313065148222…11478583318340389119

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

1.224 × 10⁹⁵(96-digit number)

12240364313065148222…11478583318340389119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.224 × 10⁹⁵(96-digit number)

12240364313065148222…11478583318340389121

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

2.448 × 10⁹⁵(96-digit number)

24480728626130296445…22957166636680778239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.448 × 10⁹⁵(96-digit number)

24480728626130296445…22957166636680778241

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

4.896 × 10⁹⁵(96-digit number)

48961457252260592891…45914333273361556479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.896 × 10⁹⁵(96-digit number)

48961457252260592891…45914333273361556481

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

9.792 × 10⁹⁵(96-digit number)

97922914504521185782…91828666546723112959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.792 × 10⁹⁵(96-digit number)

97922914504521185782…91828666546723112961

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

1.958 × 10⁹⁶(97-digit number)

19584582900904237156…83657333093446225919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.958 × 10⁹⁶(97-digit number)

19584582900904237156…83657333093446225921

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

3.916 × 10⁹⁶(97-digit number)

39169165801808474313…67314666186892451839

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 #2,262,367

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