Block #1,087,919

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/3/2015, 7:06:34 AM · Difficulty 10.7521 · 5,717,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0dd5612300d842beb3e11b56359956b13aafae749870e5f7e4cc82b64826b8d

View on Chainz ↗

Height

#1,087,919

Difficulty

10.752146

Transactions

Size

243 B

Version

Bits

0ac08c9e

Nonce

67,525,409

Timestamp

6/3/2015, 7:06:34 AM

Confirmations

5,717,828

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

8fee92800ce53f2601a626f5c5ad8a720e920b772d8c093f1d5168fa024a8357

Transactions (1)

Coinbase8fee92800ce53f…5168fa024a8357

1 in → 2 out8.6400 XPM152 B

APGBorYS…QnZrTNSi ALPu3s2c…EJXLjVFh

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.

1.285 × 10⁹⁶(97-digit number)

12850614908788505217…48913231283830625919

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

1.285 × 10⁹⁶(97-digit number)

12850614908788505217…48913231283830625919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.285 × 10⁹⁶(97-digit number)

12850614908788505217…48913231283830625921

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

2.570 × 10⁹⁶(97-digit number)

25701229817577010434…97826462567661251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.570 × 10⁹⁶(97-digit number)

25701229817577010434…97826462567661251841

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

5.140 × 10⁹⁶(97-digit number)

51402459635154020869…95652925135322503679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.140 × 10⁹⁶(97-digit number)

51402459635154020869…95652925135322503681

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

1.028 × 10⁹⁷(98-digit number)

10280491927030804173…91305850270645007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.028 × 10⁹⁷(98-digit number)

10280491927030804173…91305850270645007361

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

2.056 × 10⁹⁷(98-digit number)

20560983854061608347…82611700541290014719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.056 × 10⁹⁷(98-digit number)

20560983854061608347…82611700541290014721

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