Block #1,128,294

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/27/2015, 7:25:57 AM · Difficulty 10.9224 · 5,679,670 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eaa3890e30759ebd3683b721f0918befb75a095864fc3e82e7b65849cacd3e67

View on Chainz ↗

Height

#1,128,294

Difficulty

10.922354

Transactions

Size

654 B

Version

Bits

0aec1f67

Nonce

1,198,161,371

Timestamp

6/27/2015, 7:25:57 AM

Confirmations

5,679,670

Mined by

⛏️ P2SHAVeyoWYHyADmALV76zrnHeryCPYTYY2pr7

Merkle Root

a880dae81f81a34cc08f5296d2d37658c3914eed2cef5068545a3eb5e3d5d25b

Transactions (3)

Coinbasede715300ff7541…ece8192e6a40b0

1 in → 1 out8.3900 XPM110 B

AVeyoWYH…YTYY2pr7

c535e1da1d0c6f…34c0c7b9c717d2

1 in → 2 out3.2677 XPM227 B

AL5Ytgxh…sD9HBzMH APCDNTB3…ykwyrxY8

2ac048c5435c31…a2afc3a01e614e

1 in → 2 out2.6992 XPM225 B

AYgurPAh…pyYhLYNi Ae7YXEyn…hnSYZsCr

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.

2.947 × 10⁹⁸(99-digit number)

29474718220666675812…72516357350123110399

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

2.947 × 10⁹⁸(99-digit number)

29474718220666675812…72516357350123110399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.947 × 10⁹⁸(99-digit number)

29474718220666675812…72516357350123110401

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

5.894 × 10⁹⁸(99-digit number)

58949436441333351624…45032714700246220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.894 × 10⁹⁸(99-digit number)

58949436441333351624…45032714700246220801

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

1.178 × 10⁹⁹(100-digit number)

11789887288266670324…90065429400492441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.178 × 10⁹⁹(100-digit number)

11789887288266670324…90065429400492441601

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

2.357 × 10⁹⁹(100-digit number)

23579774576533340649…80130858800984883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.357 × 10⁹⁹(100-digit number)

23579774576533340649…80130858800984883201

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

4.715 × 10⁹⁹(100-digit number)

47159549153066681299…60261717601969766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.715 × 10⁹⁹(100-digit number)

47159549153066681299…60261717601969766401

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

9.431 × 10⁹⁹(100-digit number)

94319098306133362598…20523435203939532799

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 #1,128,294

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