Block #1,592,271

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2016, 3:05:35 AM · Difficulty 10.6494 · 5,251,340 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a10c8b64449140fdcc8b3c1ef2b98408a22ba77d6c1c27eddbfa768bdf31549f

View on Chainz ↗

Height

#1,592,271

Difficulty

10.649413

Transactions

Size

1.08 KB

Version

Bits

0aa63fe7

Nonce

353,011,088

Timestamp

5/20/2016, 3:05:35 AM

Confirmations

5,251,340

Mined by

⛏️ P2SHAdogQDU1mwnHVwaARvc1vmsfdmTs7N1gNN

Merkle Root

9fe21e0b79c91a2dbcc011cf22356f3b174178ea07540176c21e2f1027753652

Transactions (2)

Coinbase35543471469e77…9caa004d1842d6

1 in → 1 out8.8100 XPM109 B

AdogQDU1…Ts7N1gNN

8680d6b5af2030…1f06bd756d4e19

1 in → 22 out108.9080 XPM906 B

Ab8wxBvW…iiDgN5Aa AXn94E9d…xKzG1Yrs AccnWrzw…bSgkQvTU Aafcxw9H…XDKK4Qmu AGn3iwez…HFSRE9W6

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.

5.473 × 10⁹³(94-digit number)

54731402867545519351…20304371609000847999

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

5.473 × 10⁹³(94-digit number)

54731402867545519351…20304371609000847999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.473 × 10⁹³(94-digit number)

54731402867545519351…20304371609000848001

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

1.094 × 10⁹⁴(95-digit number)

10946280573509103870…40608743218001695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.094 × 10⁹⁴(95-digit number)

10946280573509103870…40608743218001696001

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

2.189 × 10⁹⁴(95-digit number)

21892561147018207740…81217486436003391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.189 × 10⁹⁴(95-digit number)

21892561147018207740…81217486436003392001

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

4.378 × 10⁹⁴(95-digit number)

43785122294036415481…62434972872006783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.378 × 10⁹⁴(95-digit number)

43785122294036415481…62434972872006784001

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

8.757 × 10⁹⁴(95-digit number)

87570244588072830962…24869945744013567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.757 × 10⁹⁴(95-digit number)

87570244588072830962…24869945744013568001

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 #1,592,271

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