Block #469,554

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 7:46:19 AM · Difficulty 10.4274 · 6,335,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c266d13af8f8916dc8db8d62516a9a24f038c667ee8051572aed7fafa9be46c0

View on Chainz ↗

Height

#469,554

Difficulty

10.427384

Transactions

Size

976 B

Version

Bits

0a6d6904

Nonce

8,582

Timestamp

4/1/2014, 7:46:19 AM

Confirmations

6,335,645

Mined by

⛏️ P2SHAUfnf7iuE8nFmCsh3aAdS7Nbkc6Vvg79hJ

Merkle Root

ac4cb3ceb11b9bcb0729ae0d4aedf6e2ae39aecbac9221d5d2c4137e21a82d06

Transactions (2)

Coinbase0ecc77721acc11…a121098dfa9df2

1 in → 1 out9.1900 XPM111 B

AUfnf7iu…6Vvg79hJ

f8959e775192e1…70760998e0cc15

4 in → 9 out36.7600 XPM774 B

AcrLeg9u…hFnsjy5L AWQhak32…eArVqMxc AVm19jL4…XmLKAj6F AeKNrjNj…1NEq95Ta AK2c7Mwr…iVRQjN8q

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.

1.315 × 10⁹⁸(99-digit number)

13153412477811146954…03689012398496666359

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

1.315 × 10⁹⁸(99-digit number)

13153412477811146954…03689012398496666359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.315 × 10⁹⁸(99-digit number)

13153412477811146954…03689012398496666361

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

2.630 × 10⁹⁸(99-digit number)

26306824955622293909…07378024796993332719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.630 × 10⁹⁸(99-digit number)

26306824955622293909…07378024796993332721

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

5.261 × 10⁹⁸(99-digit number)

52613649911244587818…14756049593986665439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.261 × 10⁹⁸(99-digit number)

52613649911244587818…14756049593986665441

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

1.052 × 10⁹⁹(100-digit number)

10522729982248917563…29512099187973330879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.052 × 10⁹⁹(100-digit number)

10522729982248917563…29512099187973330881

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

2.104 × 10⁹⁹(100-digit number)

21045459964497835127…59024198375946661759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.104 × 10⁹⁹(100-digit number)

21045459964497835127…59024198375946661761

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