Block #1,755,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/9/2016, 10:21:46 PM · Difficulty 10.7077 · 5,087,633 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c741038227db6fd1481d406b26ca2b666597f00c69ab036878fe330374ab40e

View on Chainz ↗

Height

#1,755,522

Difficulty

10.707654

Transactions

Size

1.33 KB

Version

Bits

0ab528ce

Nonce

656,838,188

Timestamp

9/9/2016, 10:21:46 PM

Confirmations

5,087,633

Mined by

⛏️ P2SHAcNpanC3paPgrPmB8hC2tcNyxpZksfAsLB

Merkle Root

448821200303d04eacb785d14373e686f60d883d18ee6174be98428e0f973af8

Transactions (3)

Coinbase009a9d8d346022…0a98f03c3d5089

1 in → 1 out8.7300 XPM110 B

AcNpanC3…ZksfAsLB

74c837332aac6c…1afa271635d1ec

4 in → 1 out1725.9900 XPM636 B

AcDhjHA9…ebukETHz

158d6f2c695971…f3f97eb04f6b2b

3 in → 2 out25.1779 XPM521 B

AYEWR4Hw…6H3DrDBM AMHrkDr2…YXJ2SqfX

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.

6.592 × 10⁹⁷(98-digit number)

65924517722822755303…10389621940581498879

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

6.592 × 10⁹⁷(98-digit number)

65924517722822755303…10389621940581498879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.592 × 10⁹⁷(98-digit number)

65924517722822755303…10389621940581498881

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

1.318 × 10⁹⁸(99-digit number)

13184903544564551060…20779243881162997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.318 × 10⁹⁸(99-digit number)

13184903544564551060…20779243881162997761

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

2.636 × 10⁹⁸(99-digit number)

26369807089129102121…41558487762325995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.636 × 10⁹⁸(99-digit number)

26369807089129102121…41558487762325995521

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

5.273 × 10⁹⁸(99-digit number)

52739614178258204242…83116975524651991039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.273 × 10⁹⁸(99-digit number)

52739614178258204242…83116975524651991041

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

1.054 × 10⁹⁹(100-digit number)

10547922835651640848…66233951049303982079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.054 × 10⁹⁹(100-digit number)

10547922835651640848…66233951049303982081

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 #1,755,522

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