Block #665,653

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/6/2014, 3:08:40 PM · Difficulty 10.9601 · 6,141,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb89a59a6f23949b562090f5fd3bc10d13673949e000b347e0a4eaf641369d64

View on Chainz ↗

Height

#665,653

Difficulty

10.960121

Transactions

Size

806 B

Version

Bits

0af5ca80

Nonce

1,845,311,620

Timestamp

8/6/2014, 3:08:40 PM

Confirmations

6,141,311

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f77708a51ecd03e685f30e56dbf1e594a2b861beb1b0cc37b53b65ef9f53cb1b

Transactions (3)

Coinbase53c492ea0ec976…f00762719b3adc

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

f2906bbcebed9e…9f6683f9396da8

2 in → 2 out13.5667 XPM374 B

AZFyR8n4…Xiiavx12 AdSWQQqx…eYDM88pb

1b2c89a931d332…6a8e696483e81c

1 in → 2 out3.5252 XPM225 B

AZknZb9b…bVU5VHFw AVLHeigJ…tQ6QQ9DY

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.

2.458 × 10⁹⁶(97-digit number)

24588293197306658199…70398081436471487999

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

2.458 × 10⁹⁶(97-digit number)

24588293197306658199…70398081436471487999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.458 × 10⁹⁶(97-digit number)

24588293197306658199…70398081436471488001

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

4.917 × 10⁹⁶(97-digit number)

49176586394613316399…40796162872942975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.917 × 10⁹⁶(97-digit number)

49176586394613316399…40796162872942976001

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

9.835 × 10⁹⁶(97-digit number)

98353172789226632798…81592325745885951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.835 × 10⁹⁶(97-digit number)

98353172789226632798…81592325745885952001

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

1.967 × 10⁹⁷(98-digit number)

19670634557845326559…63184651491771903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.967 × 10⁹⁷(98-digit number)

19670634557845326559…63184651491771904001

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

3.934 × 10⁹⁷(98-digit number)

39341269115690653119…26369302983543807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.934 × 10⁹⁷(98-digit number)

39341269115690653119…26369302983543808001

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

7.868 × 10⁹⁷(98-digit number)

78682538231381306239…52738605967087615999

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 #665,653

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