Block #1,304,066

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 10/29/2015, 6:22:24 PM · Difficulty 10.8535 · 5,504,159 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1687b562a388611456575128d9cdcc1ee9bc0d8b1ef8761dfffac73add6dc42c

View on Chainz ↗

Height

#1,304,066

Difficulty

10.853535

Transactions

Size

70.36 KB

Version

Bits

0ada8143

Nonce

1,752,538,080

Timestamp

10/29/2015, 6:22:24 PM

Confirmations

5,504,159

Mined by

⛏️ P2SHAdb9ckrCGQTCYT6hUFx7L1bJZLboKSN5u4

Merkle Root

00c6a3e63534db39856919e98820fba8be5d35f30e37d5a16b9eaf95cdb73a17

Transactions (2)

Coinbaseb70a78c833a067…6600141f00bb32

1 in → 1 out9.4200 XPM110 B

Adb9ckrC…boKSN5u4

81a7f905f5ecbd…fcfc4b85b99ad4

485 in → 2 out110.1901 XPM70.16 KB

AQHE5e6H…xDwU3vYU AVuniwQB…F2tqJPn6

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.

1.280 × 10⁹⁵(96-digit number)

12806792765657612235…81133036360664772959

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

1.280 × 10⁹⁵(96-digit number)

12806792765657612235…81133036360664772959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.280 × 10⁹⁵(96-digit number)

12806792765657612235…81133036360664772961

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

2.561 × 10⁹⁵(96-digit number)

25613585531315224470…62266072721329545919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.561 × 10⁹⁵(96-digit number)

25613585531315224470…62266072721329545921

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

5.122 × 10⁹⁵(96-digit number)

51227171062630448940…24532145442659091839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.122 × 10⁹⁵(96-digit number)

51227171062630448940…24532145442659091841

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

1.024 × 10⁹⁶(97-digit number)

10245434212526089788…49064290885318183679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.024 × 10⁹⁶(97-digit number)

10245434212526089788…49064290885318183681

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

2.049 × 10⁹⁶(97-digit number)

20490868425052179576…98128581770636367359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.049 × 10⁹⁶(97-digit number)

20490868425052179576…98128581770636367361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.098 × 10⁹⁶(97-digit number)

40981736850104359152…96257163541272734719

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.098 × 10⁹⁶(97-digit number)

40981736850104359152…96257163541272734721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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

Block #1,304,066

Cookie Preferences