Block #150,060

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 6:56:13 PM · Difficulty 9.8583 · 6,645,865 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d95dcfa22ffed57942facb39954e9aad339b6d868afe9257d37c395599b10e6c

View on Chainz ↗

Height

#150,060

Difficulty

9.858269

Transactions

Size

731 B

Version

Bits

09dbb78b

Nonce

30,674

Timestamp

9/4/2013, 6:56:13 PM

Confirmations

6,645,865

Mined by

⛏️ P2SHAes3gGUmswPaSPz1TaBngRjCG83Ud68cAG

Merkle Root

fb27acc46a57bee0be5c5f7eedbace7f99058ad7ada36bf496ceeff08a0458d1

Transactions (3)

Coinbase8455ed1696daef…f44ba063209d2a

1 in → 1 out10.2900 XPM109 B

Aes3gGUm…3Ud68cAG

1609553d38d199…dcd0fb5e51d37b

2 in → 2 out400.0123 XPM373 B

AMeC6CFj…T6z7aMTQ AWD4VgHE…qxX9q4vi

164e1419919bfd…968f102fb6df47

1 in → 1 out10.3400 XPM157 B

ATrGqBKA…Ev1i3JEB

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.

3.138 × 10⁹⁸(99-digit number)

31381244321562950915…81506334959037503999

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

3.138 × 10⁹⁸(99-digit number)

31381244321562950915…81506334959037503999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.138 × 10⁹⁸(99-digit number)

31381244321562950915…81506334959037504001

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

6.276 × 10⁹⁸(99-digit number)

62762488643125901831…63012669918075007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.276 × 10⁹⁸(99-digit number)

62762488643125901831…63012669918075008001

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

1.255 × 10⁹⁹(100-digit number)

12552497728625180366…26025339836150015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.255 × 10⁹⁹(100-digit number)

12552497728625180366…26025339836150016001

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

2.510 × 10⁹⁹(100-digit number)

25104995457250360732…52050679672300031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.510 × 10⁹⁹(100-digit number)

25104995457250360732…52050679672300032001

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

5.020 × 10⁹⁹(100-digit number)

50209990914500721465…04101359344600063999

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