Block #2,731,508

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/2/2018, 8:06:27 PM · Difficulty 11.6317 · 4,111,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ea0af58cf71cec6f33e4eb1b71b835b8d8f2d7366b367d8efd3e3fe9e796fc4

View on Chainz ↗

Height

#2,731,508

Difficulty

11.631669

Transactions

Size

458 B

Version

Bits

0ba1b507

Nonce

645,680,534

Timestamp

7/2/2018, 8:06:27 PM

Confirmations

4,111,983

Mined by

⛏️ P2SHAV2iojwGsdjC12o6Pm6A3z5vNcKbAg6Fub

Merkle Root

e03e831cc2e278b39d04276fce1282df9d5b3c34484d5d9e71f3068608c1c3d1

Transactions (2)

Coinbase6b66dcaa3f0a71…18b080916f9e2e

1 in → 1 out7.3900 XPM109 B

AV2iojwG…KbAg6Fub

37283003a2afa7…6440f5cc82c65f

1 in → 3 out15.4414 XPM259 B

AXyjLdPn…7ott1WzB AazM9Tys…BPTQzcnq AGqT4L9Q…bw8Y6MGy

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.

1.107 × 10⁹⁴(95-digit number)

11076928081735262894…75162821940049440079

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

1.107 × 10⁹⁴(95-digit number)

11076928081735262894…75162821940049440079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10⁹⁴(95-digit number)

11076928081735262894…75162821940049440081

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

2.215 × 10⁹⁴(95-digit number)

22153856163470525789…50325643880098880159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.215 × 10⁹⁴(95-digit number)

22153856163470525789…50325643880098880161

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

4.430 × 10⁹⁴(95-digit number)

44307712326941051578…00651287760197760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.430 × 10⁹⁴(95-digit number)

44307712326941051578…00651287760197760321

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

8.861 × 10⁹⁴(95-digit number)

88615424653882103156…01302575520395520639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.861 × 10⁹⁴(95-digit number)

88615424653882103156…01302575520395520641

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

1.772 × 10⁹⁵(96-digit number)

17723084930776420631…02605151040791041279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.772 × 10⁹⁵(96-digit number)

17723084930776420631…02605151040791041281

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

3.544 × 10⁹⁵(96-digit number)

35446169861552841262…05210302081582082559

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

Block #2,731,508

Cookie Preferences