Block #756,780

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/8/2014, 1:05:19 PM · Difficulty 10.9670 · 6,070,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7c4d06e2035d892555455c4a2eb7f6edf5f750efea671b0af38eb20c29a6f1a

View on Chainz ↗

Height

#756,780

Difficulty

10.966999

Transactions

Size

583 B

Version

Bits

0af78d44

Nonce

934,998,573

Timestamp

10/8/2014, 1:05:19 PM

Confirmations

6,070,210

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9504cbe4357e8e301496df3689e179aa221c20041985625f6fe775da87c15363

Transactions (2)

Coinbase2cc604661d6ed9…6df7654d1b2d85

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

b6d7af00548b43…e02f2c3db112f8

2 in → 2 out2.5334 XPM376 B

AGqSWjWQ…gzSSkRFQ AeKNrjNj…1NEq95Ta

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.

1.275 × 10⁹⁸(99-digit number)

12750783612568718979…05977902959465983999

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

1.275 × 10⁹⁸(99-digit number)

12750783612568718979…05977902959465983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10⁹⁸(99-digit number)

12750783612568718979…05977902959465984001

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

2.550 × 10⁹⁸(99-digit number)

25501567225137437958…11955805918931967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.550 × 10⁹⁸(99-digit number)

25501567225137437958…11955805918931968001

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

5.100 × 10⁹⁸(99-digit number)

51003134450274875917…23911611837863935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.100 × 10⁹⁸(99-digit number)

51003134450274875917…23911611837863936001

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

1.020 × 10⁹⁹(100-digit number)

10200626890054975183…47823223675727871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁹(100-digit number)

10200626890054975183…47823223675727872001

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

2.040 × 10⁹⁹(100-digit number)

20401253780109950367…95646447351455743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.040 × 10⁹⁹(100-digit number)

20401253780109950367…95646447351455744001

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

4.080 × 10⁹⁹(100-digit number)

40802507560219900734…91292894702911487999

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 #756,780

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