Block #1,250,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/24/2015, 4:58:25 AM · Difficulty 10.7747 · 5,574,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26c6e2a33f7bb0526f1b1ab4d9261b559f7ba5f98c52951245955a51b284b15b

View on Chainz ↗

Height

#1,250,746

Difficulty

10.774745

Transactions

Size

1.72 KB

Version

Bits

0ac655ad

Nonce

842,831,869

Timestamp

9/24/2015, 4:58:25 AM

Confirmations

5,574,814

Mined by

⛏️ P2SHAJcWcfmEJguL3gW6TqfAVUkWWkFHAdQNMM

Merkle Root

ae6222c62f3ebaf9feb222eb31341e5f93254b728e516f6f0be1fea094dc16f6

Transactions (2)

Coinbase0e30d33dac342c…3001933b6c139a

1 in → 1 out8.6200 XPM110 B

AJcWcfmE…FHAdQNMM

94c117127c178c…c133872ab7b7b4

10 in → 2 out240.3575 XPM1.52 KB

ATTvz9zo…eWm5t22d AUXRxsGg…Lbe6QQft

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.

1.875 × 10⁹⁸(99-digit number)

18750332514173752448…44808877622878207999

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

1.875 × 10⁹⁸(99-digit number)

18750332514173752448…44808877622878207999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.875 × 10⁹⁸(99-digit number)

18750332514173752448…44808877622878208001

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

3.750 × 10⁹⁸(99-digit number)

37500665028347504897…89617755245756415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.750 × 10⁹⁸(99-digit number)

37500665028347504897…89617755245756416001

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

7.500 × 10⁹⁸(99-digit number)

75001330056695009795…79235510491512831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.500 × 10⁹⁸(99-digit number)

75001330056695009795…79235510491512832001

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

1.500 × 10⁹⁹(100-digit number)

15000266011339001959…58471020983025663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.500 × 10⁹⁹(100-digit number)

15000266011339001959…58471020983025664001

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

3.000 × 10⁹⁹(100-digit number)

30000532022678003918…16942041966051327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.000 × 10⁹⁹(100-digit number)

30000532022678003918…16942041966051328001

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 #1,250,746

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