Block #1,225,348

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2015, 2:34:32 AM · Difficulty 10.7365 · 5,570,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2174c9d6696403f7f14f36d20a528f4cc24a95a6c0d84ec20041a5b160466c12

View on Chainz ↗

Height

#1,225,348

Difficulty

10.736507

Transactions

Size

1.00 KB

Version

Bits

0abc8bbd

Nonce

553,967,248

Timestamp

9/7/2015, 2:34:32 AM

Confirmations

5,570,150

Mined by

⛏️ P2SHAJz1ycRgHxNBBDrPPakNv8KJTxduKEXfXc

Merkle Root

b3658d06547642b616eba8b51ae21c11b25b40091ca0d8d876470e139379af0b

Transactions (4)

Coinbase66b2b362d0e375…fa6c008e80782b

1 in → 1 out8.6900 XPM110 B

AJz1ycRg…duKEXfXc

f20f015546aa6f…a288c96a986b72

1 in → 2 out8.6400 XPM226 B

ATz6VVQn…zBfUvcQh AG3TPGas…cJvesb2o

08f8ac18ccd985…a5cc8f5a95f9ec

2 in → 2 out13.4305 XPM375 B

AJrav1hc…H96vkAEd AZpeGnSF…4cbyDNBL

f54d1f6ea633f3…fa9db476edf9b1

1 in → 2 out6.5438 XPM227 B

AcuM7XiJ…5uND8Jce AGFLavUG…EZx956Sa

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.

6.583 × 10⁹⁶(97-digit number)

65833997543371046031…31615943997536788479

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

6.583 × 10⁹⁶(97-digit number)

65833997543371046031…31615943997536788479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.583 × 10⁹⁶(97-digit number)

65833997543371046031…31615943997536788481

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

1.316 × 10⁹⁷(98-digit number)

13166799508674209206…63231887995073576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.316 × 10⁹⁷(98-digit number)

13166799508674209206…63231887995073576961

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

2.633 × 10⁹⁷(98-digit number)

26333599017348418412…26463775990147153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.633 × 10⁹⁷(98-digit number)

26333599017348418412…26463775990147153921

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

5.266 × 10⁹⁷(98-digit number)

52667198034696836825…52927551980294307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.266 × 10⁹⁷(98-digit number)

52667198034696836825…52927551980294307841

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

1.053 × 10⁹⁸(99-digit number)

10533439606939367365…05855103960588615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.053 × 10⁹⁸(99-digit number)

10533439606939367365…05855103960588615681

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