Block #152,380

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/6/2013, 7:13:29 AM · Difficulty 9.8623 · 6,643,782 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f76f43a488255d9e9a8bb7e37b5c702efe903182076a832778039d559490c4fe

View on Chainz ↗

Height

#152,380

Difficulty

9.862260

Transactions

Size

2.55 KB

Version

Bits

09dcbd16

Nonce

29,446

Timestamp

9/6/2013, 7:13:29 AM

Confirmations

6,643,782

Mined by

⛏️ P2SHAT9d5vjomgTLEuzVWBeXXxP8HGGhkmqfrQ

Merkle Root

d9f4ebb3206a554083795ca500a122f54011fa57d3aad7d9852b206e2eea3000

Transactions (4)

Coinbaseb3ce306514c66a…753ff662af0e11

1 in → 1 out10.3200 XPM109 B

AT9d5vjo…GhkmqfrQ

c853a7bf612580…f468ad77bf1704

1 in → 1 out514.1500 XPM192 B

AbxSykSg…BX71twYi

0639a1e2133367…abeccbc7cb921e

9 in → 2 out109.0449 XPM1.38 KB

AXTZzW5k…MChmii15 AK3x8dvE…nYbmJccD

0e8ab66c8c8ce0…50e596bf244dd0

5 in → 2 out5.0789 XPM815 B

APauQY31…RTyPnhYP AHLqQjYK…4CDrWv66

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.

1.040 × 10⁹³(94-digit number)

10407185179546592027…64237489413344272639

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

1.040 × 10⁹³(94-digit number)

10407185179546592027…64237489413344272639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.040 × 10⁹³(94-digit number)

10407185179546592027…64237489413344272641

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

2.081 × 10⁹³(94-digit number)

20814370359093184055…28474978826688545279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.081 × 10⁹³(94-digit number)

20814370359093184055…28474978826688545281

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

4.162 × 10⁹³(94-digit number)

41628740718186368111…56949957653377090559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.162 × 10⁹³(94-digit number)

41628740718186368111…56949957653377090561

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

8.325 × 10⁹³(94-digit number)

83257481436372736222…13899915306754181119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.325 × 10⁹³(94-digit number)

83257481436372736222…13899915306754181121

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

1.665 × 10⁹⁴(95-digit number)

16651496287274547244…27799830613508362239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.665 × 10⁹⁴(95-digit number)

16651496287274547244…27799830613508362241

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