Block #1,239,710

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/16/2015, 6:59:14 PM · Difficulty 10.7580 · 5,603,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ccdd9d0e6d33f14fa1b13bba819a15c2019e1f739e18d57bd1d45ca21fdf7e5

View on Chainz ↗

Height

#1,239,710

Difficulty

10.758007

Transactions

Size

4.11 KB

Version

Bits

0ac20cbf

Nonce

324,646,375

Timestamp

9/16/2015, 6:59:14 PM

Confirmations

5,603,591

Mined by

⛏️ P2SHAMXyqmkE3XQ9eevwT4dsVZPC2UJgjAaWsh

Merkle Root

d19748615f24b2cd330a5c25ef4fe3b3b8ae7be8fe842083fb983aac5df263ef

Transactions (3)

Coinbase56052e6b416011…958345c18aa46d

1 in → 1 out8.7200 XPM110 B

AMXyqmkE…JgjAaWsh

8d355fef33dde4…8db50f87d02526

24 in → 2 out244.1265 XPM3.55 KB

AQ8obrRF…hCezsXdr APXizGYE…kSPJVy4U

ff466ad6cf2aff…4ffe21b817de96

2 in → 2 out11.0608 XPM373 B

AZpeGnSF…4cbyDNBL ALEw3YYr…m9F82L5U

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.

1.528 × 10⁹⁷(98-digit number)

15281103221608730440…21006760742009569279

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

1.528 × 10⁹⁷(98-digit number)

15281103221608730440…21006760742009569279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.528 × 10⁹⁷(98-digit number)

15281103221608730440…21006760742009569281

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

3.056 × 10⁹⁷(98-digit number)

30562206443217460881…42013521484019138559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.056 × 10⁹⁷(98-digit number)

30562206443217460881…42013521484019138561

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

6.112 × 10⁹⁷(98-digit number)

61124412886434921762…84027042968038277119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.112 × 10⁹⁷(98-digit number)

61124412886434921762…84027042968038277121

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

1.222 × 10⁹⁸(99-digit number)

12224882577286984352…68054085936076554239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.222 × 10⁹⁸(99-digit number)

12224882577286984352…68054085936076554241

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

2.444 × 10⁹⁸(99-digit number)

24449765154573968705…36108171872153108479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.444 × 10⁹⁸(99-digit number)

24449765154573968705…36108171872153108481

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 #1,239,710

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