Block #1,254,097

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/26/2015, 5:39:31 AM · Difficulty 10.7933 · 5,555,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be6fbf225d066fe0e7adcb472522d0ca37c06e456a9bb1d8afdfc59777d6e723

View on Chainz ↗

Height

#1,254,097

Difficulty

10.793304

Transactions

Size

1.00 KB

Version

Bits

0acb15fb

Nonce

49,680,827

Timestamp

9/26/2015, 5:39:31 AM

Confirmations

5,555,610

Mined by

⛏️ P2SHAYJW4YE3i638KSU7JKZEhHSSB1W5bfVmd6

Merkle Root

b3eac67cfd6fdab55176bb214e830bc758f31aebd33b61a36dc9e84160287037

Transactions (4)

Coinbase486ccba441c7d9…a9861b5976cab7

1 in → 1 out8.6000 XPM109 B

AYJW4YE3…W5bfVmd6

9481f38894218f…bbe5bda397a710

1 in → 2 out8.5900 XPM226 B

ALMHufcS…mHkKzgnF ANRBzdDL…FmZX4CN6

d003c827bbb48f…1a03b472883e48

1 in → 2 out8.5900 XPM227 B

ANwc8yy5…D8xqqDWC ATAHFtMj…hBmSdXaQ

a10a44e59602cf…98c44ab9f05631

2 in → 2 out5.2941 XPM375 B

AMHK5Hy6…fiBMiLxK AaVKB9je…EGKseGJV

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.

7.010 × 10⁹²(93-digit number)

70106787995162478887…32239717832132347199

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

7.010 × 10⁹²(93-digit number)

70106787995162478887…32239717832132347199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.010 × 10⁹²(93-digit number)

70106787995162478887…32239717832132347201

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

1.402 × 10⁹³(94-digit number)

14021357599032495777…64479435664264694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.402 × 10⁹³(94-digit number)

14021357599032495777…64479435664264694401

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

2.804 × 10⁹³(94-digit number)

28042715198064991554…28958871328529388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.804 × 10⁹³(94-digit number)

28042715198064991554…28958871328529388801

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

5.608 × 10⁹³(94-digit number)

56085430396129983109…57917742657058777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.608 × 10⁹³(94-digit number)

56085430396129983109…57917742657058777601

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

1.121 × 10⁹⁴(95-digit number)

11217086079225996621…15835485314117555199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.121 × 10⁹⁴(95-digit number)

11217086079225996621…15835485314117555201

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

Block #1,254,097

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