Block #1,288,234

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/19/2015, 5:46:38 AM · Difficulty 10.8319 · 5,553,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6ac45b8dd73defea9800b68b634d3bda97d5b2b317c84717f078c3a4b6982ce

View on Chainz ↗

Height

#1,288,234

Difficulty

10.831885

Transactions

Size

11.66 KB

Version

Bits

0ad4f66b

Nonce

500,924,457

Timestamp

10/19/2015, 5:46:38 AM

Confirmations

5,553,796

Mined by

⛏️ P2SHAW99eWpTWwnYD9oRACLB9fnUHoqGBpdkH7

Merkle Root

7e11fdf2676c1de56baa8540db86eabd95af4dd188e83c38a9302c77756ed1ed

Transactions (2)

Coinbaseefb2bc6a011595…b7ef7901304516

1 in → 1 out8.7200 XPM110 B

AW99eWpT…qGBpdkH7

6f129d1768cec9…9a503dc0d86845

79 in → 1 out1435.3157 XPM11.46 KB

AQ8obrRF…hCezsXdr

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.

2.007 × 10⁹⁶(97-digit number)

20071515786502462984…51892638335811719679

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

2.007 × 10⁹⁶(97-digit number)

20071515786502462984…51892638335811719679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.007 × 10⁹⁶(97-digit number)

20071515786502462984…51892638335811719681

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

4.014 × 10⁹⁶(97-digit number)

40143031573004925968…03785276671623439359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.014 × 10⁹⁶(97-digit number)

40143031573004925968…03785276671623439361

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

8.028 × 10⁹⁶(97-digit number)

80286063146009851936…07570553343246878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.028 × 10⁹⁶(97-digit number)

80286063146009851936…07570553343246878721

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

1.605 × 10⁹⁷(98-digit number)

16057212629201970387…15141106686493757439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.605 × 10⁹⁷(98-digit number)

16057212629201970387…15141106686493757441

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

3.211 × 10⁹⁷(98-digit number)

32114425258403940774…30282213372987514879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.211 × 10⁹⁷(98-digit number)

32114425258403940774…30282213372987514881

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 #1,288,234

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