Block #154,647

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 7:43:27 PM · Difficulty 9.8645 · 6,635,341 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

20b4645d084c6ec715836bd18a9bcf4a232b08bd3b4c5a6eaa3e441ac560ea90

View on Chainz ↗

Height

#154,647

Difficulty

9.864473

Transactions

Size

1.66 KB

Version

Bits

09dd4e21

Nonce

160,369

Timestamp

9/7/2013, 7:43:27 PM

Confirmations

6,635,341

Merkle Root

5b52577200d94806a0ec672ef79d8dec365c3a19c0267fead3eb1e90f87d061d

Transactions (5)

Coinbase6a87fca0ac0cab…3e87c01e8c73fc

1 in → 1 out10.3100 XPM109 B

AWtz5HSy…LU5zbcaL

26286b1fcd90ef…360bb91739827b

1 in → 2 out10.2600 XPM226 B

AYQGXzXW…9eggLvJE ARbmBPFw…TKD9QyDt

639003335cbc9b…681d427d1f20b6

1 in → 2 out8.2253 XPM227 B

AcN7Mwej…Rnr1man2 Adf5iUrP…hnB7kqy9

3c16c4ec86475e…4978a85ab943b1

1 in → 2 out5.7498 XPM227 B

AKkhT67J…hkT5NbDb AXwKKGcU…yK2w3TwR

9a68cc65d1c3a6…bedc0ea824bbf7

5 in → 2 out2.0721 XPM818 B

ALz3uSwR…DHKjj4EL AbGBEVU3…3iNMW4Lk

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.

2.368 × 10⁹³(94-digit number)

23682133435910774025…33936772922347623999

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

2.368 × 10⁹³(94-digit number)

23682133435910774025…33936772922347623999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.368 × 10⁹³(94-digit number)

23682133435910774025…33936772922347624001

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

4.736 × 10⁹³(94-digit number)

47364266871821548050…67873545844695247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.736 × 10⁹³(94-digit number)

47364266871821548050…67873545844695248001

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

9.472 × 10⁹³(94-digit number)

94728533743643096100…35747091689390495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.472 × 10⁹³(94-digit number)

94728533743643096100…35747091689390496001

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

1.894 × 10⁹⁴(95-digit number)

18945706748728619220…71494183378780991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.894 × 10⁹⁴(95-digit number)

18945706748728619220…71494183378780992001

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

3.789 × 10⁹⁴(95-digit number)

37891413497457238440…42988366757561983999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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