Block #693,528

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/26/2014, 9:05:03 AM · Difficulty 10.9564 · 6,116,049 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

557e18f955166241ebf8234816647f86d88aefe3fa734686dafa6a38015cf794

View on Chainz ↗

Height

#693,528

Difficulty

10.956442

Transactions

Size

433 B

Version

Bits

0af4d962

Nonce

1,089,087,778

Timestamp

8/26/2014, 9:05:03 AM

Confirmations

6,116,049

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

897a85ed3f175a70fcc86b45a3364c362cf8f818a2b6647f0734b8eaea7f9e5e

Transactions (2)

Coinbase3a9c2943ba4833…df6bc27a59e41f

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

e24ca53ca841bc…79a0c20a0cd2fb

1 in → 3 out8.3100 XPM226 B

AHrFNmf8…hpqU2WtU ALeH3dPN…zVgWRzZU 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.

1.324 × 10⁹⁶(97-digit number)

13248182612356324139…60223541567868423999

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

1.324 × 10⁹⁶(97-digit number)

13248182612356324139…60223541567868423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.324 × 10⁹⁶(97-digit number)

13248182612356324139…60223541567868424001

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

2.649 × 10⁹⁶(97-digit number)

26496365224712648278…20447083135736847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.649 × 10⁹⁶(97-digit number)

26496365224712648278…20447083135736848001

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

5.299 × 10⁹⁶(97-digit number)

52992730449425296556…40894166271473695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.299 × 10⁹⁶(97-digit number)

52992730449425296556…40894166271473696001

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

1.059 × 10⁹⁷(98-digit number)

10598546089885059311…81788332542947391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.059 × 10⁹⁷(98-digit number)

10598546089885059311…81788332542947392001

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

2.119 × 10⁹⁷(98-digit number)

21197092179770118622…63576665085894783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.119 × 10⁹⁷(98-digit number)

21197092179770118622…63576665085894784001

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

4.239 × 10⁹⁷(98-digit number)

42394184359540237244…27153330171789567999

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 #693,528

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