Block #2,272,049

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/28/2017, 3:39:37 PM · Difficulty 10.9541 · 4,558,546 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13ddab93e4afb2d42d060b37e80558d03e4a05aaaaf0c4e09606c899254ff7ed

View on Chainz ↗

Height

#2,272,049

Difficulty

10.954069

Transactions

Size

424 B

Version

Bits

0af43de6

Nonce

2,051,706,056

Timestamp

8/28/2017, 3:39:37 PM

Confirmations

4,558,546

Mined by

⛏️ P2SHAJpnwRZFppaexRidNRhSWzejY1u6PgGDHw

Merkle Root

a32d5faa18b5dba04ade8821e685fdab60f3af4888f4a6003cdec72b6842448f

Transactions (2)

Coinbase4731102ea6dafa…e6b25e2b94a65e

1 in → 1 out8.3300 XPM109 B

AJpnwRZF…u6PgGDHw

ce676720015462…6164bc2a11e6b1

1 in → 2 out2.8323 XPM225 B

AV5bDXsF…JGKHA1dB AGfYzJRh…4uodP7T3

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.

6.906 × 10⁹³(94-digit number)

69068515050913338993…38838588698120003249

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

6.906 × 10⁹³(94-digit number)

69068515050913338993…38838588698120003249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.906 × 10⁹³(94-digit number)

69068515050913338993…38838588698120003251

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

1.381 × 10⁹⁴(95-digit number)

13813703010182667798…77677177396240006499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.381 × 10⁹⁴(95-digit number)

13813703010182667798…77677177396240006501

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

2.762 × 10⁹⁴(95-digit number)

27627406020365335597…55354354792480012999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.762 × 10⁹⁴(95-digit number)

27627406020365335597…55354354792480013001

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

5.525 × 10⁹⁴(95-digit number)

55254812040730671195…10708709584960025999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.525 × 10⁹⁴(95-digit number)

55254812040730671195…10708709584960026001

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

1.105 × 10⁹⁵(96-digit number)

11050962408146134239…21417419169920051999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.105 × 10⁹⁵(96-digit number)

11050962408146134239…21417419169920052001

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

2.210 × 10⁹⁵(96-digit number)

22101924816292268478…42834838339840103999

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 #2,272,049

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