Block #1,225,321

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2015, 2:08:25 AM · Difficulty 10.7365 · 5,577,735 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

232170e80c7f716a4df9961b736dac2b71f683f6002a7a2ba02573a8da2f0f48

View on Chainz ↗

Height

#1,225,321

Difficulty

10.736473

Transactions

Size

574 B

Version

Bits

0abc8984

Nonce

858,492,354

Timestamp

9/7/2015, 2:08:25 AM

Confirmations

5,577,735

Mined by

⛏️ P2SHATTAzTiu21DWs4TTZexs9Hy8KjuG2EuxVN

Merkle Root

d0cd8c0a6bfe4d8bfb22e2f6561f6c33dc28514a518f1b5b71362fa0a89f75a2

Transactions (2)

Coinbase0a4d1db70ddf78…11b451b3e127c1

1 in → 1 out8.6700 XPM109 B

ATTAzTiu…uG2EuxVN

4e177b7feaf7b2…a85339f92b166a

2 in → 2 out13.2987 XPM374 B

Af2WPCNw…2PK5fZhZ AJRwGPSP…QDRWdi2B

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.

2.696 × 10⁹⁶(97-digit number)

26963366580767610192…02372791073766458239

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

2.696 × 10⁹⁶(97-digit number)

26963366580767610192…02372791073766458239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.696 × 10⁹⁶(97-digit number)

26963366580767610192…02372791073766458241

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

5.392 × 10⁹⁶(97-digit number)

53926733161535220385…04745582147532916479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.392 × 10⁹⁶(97-digit number)

53926733161535220385…04745582147532916481

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

1.078 × 10⁹⁷(98-digit number)

10785346632307044077…09491164295065832959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.078 × 10⁹⁷(98-digit number)

10785346632307044077…09491164295065832961

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

2.157 × 10⁹⁷(98-digit number)

21570693264614088154…18982328590131665919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.157 × 10⁹⁷(98-digit number)

21570693264614088154…18982328590131665921

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

4.314 × 10⁹⁷(98-digit number)

43141386529228176308…37964657180263331839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.314 × 10⁹⁷(98-digit number)

43141386529228176308…37964657180263331841

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