Block #1,076,255

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2015, 3:42:59 AM · Difficulty 10.7546 · 5,726,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cbbb747a9bae8385025d6e4d8e3732656977df70501838e1ddb316ed7cb6953

View on Chainz ↗

Height

#1,076,255

Difficulty

10.754638

Transactions

Size

243 B

Version

Bits

0ac12ff1

Nonce

25,650,827

Timestamp

5/26/2015, 3:42:59 AM

Confirmations

5,726,244

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

8027f26696bd4db4e7ff1228d027e46d624020db410296cf891b926760a2c1b5

Transactions (1)

Coinbase8027f26696bd4d…1b926760a2c1b5

1 in → 2 out8.6300 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.

1.134 × 10⁹⁶(97-digit number)

11346032828288300354…41932631491316856319

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

1.134 × 10⁹⁶(97-digit number)

11346032828288300354…41932631491316856319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.134 × 10⁹⁶(97-digit number)

11346032828288300354…41932631491316856321

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

2.269 × 10⁹⁶(97-digit number)

22692065656576600709…83865262982633712639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.269 × 10⁹⁶(97-digit number)

22692065656576600709…83865262982633712641

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

4.538 × 10⁹⁶(97-digit number)

45384131313153201419…67730525965267425279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.538 × 10⁹⁶(97-digit number)

45384131313153201419…67730525965267425281

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

9.076 × 10⁹⁶(97-digit number)

90768262626306402839…35461051930534850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.076 × 10⁹⁶(97-digit number)

90768262626306402839…35461051930534850561

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

1.815 × 10⁹⁷(98-digit number)

18153652525261280567…70922103861069701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.815 × 10⁹⁷(98-digit number)

18153652525261280567…70922103861069701121

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

3.630 × 10⁹⁷(98-digit number)

36307305050522561135…41844207722139402239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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