Block #247,702

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 10:23:31 PM · Difficulty 9.9652 · 6,569,189 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89b27940db2d3c4a88b010e73f685072abf6b916b9b5885902ba80a022b738cd

View on Chainz ↗

Height

#247,702

Difficulty

9.965171

Transactions

Size

533 B

Version

Bits

09f7156c

Nonce

10,390

Timestamp

11/6/2013, 10:23:31 PM

Confirmations

6,569,189

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

100ef199b2d7841b9f7cffa651c8638bf8ec260eb511d34e044ac56eac85e4f6

Transactions (2)

Coinbaseecb5334f960715…1dcb06f36b4656

1 in → 2 out10.0600 XPM137 B

AZDUEbdS…RYKMRZET AHsw4d6U…EnM8UXNZ

3adab1bf99d90b…37e4f9e571331e

2 in → 2 out20.2300 XPM306 B

ARM93YUF…ExPEu9xU ANkWbo7W…xHNaGiQb

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.

1.476 × 10⁹⁵(96-digit number)

14760943930977108249…91381084659816867439

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

1.476 × 10⁹⁵(96-digit number)

14760943930977108249…91381084659816867439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.476 × 10⁹⁵(96-digit number)

14760943930977108249…91381084659816867441

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

2.952 × 10⁹⁵(96-digit number)

29521887861954216499…82762169319633734879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.952 × 10⁹⁵(96-digit number)

29521887861954216499…82762169319633734881

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

5.904 × 10⁹⁵(96-digit number)

59043775723908432998…65524338639267469759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.904 × 10⁹⁵(96-digit number)

59043775723908432998…65524338639267469761

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

1.180 × 10⁹⁶(97-digit number)

11808755144781686599…31048677278534939519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.180 × 10⁹⁶(97-digit number)

11808755144781686599…31048677278534939521

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

2.361 × 10⁹⁶(97-digit number)

23617510289563373199…62097354557069879039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.361 × 10⁹⁶(97-digit number)

23617510289563373199…62097354557069879041

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 #247,702

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