Block #710,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2014, 7:32:37 AM · Difficulty 10.9563 · 6,083,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8681cab88af6f37fa9c4a8407411ae69a5724c6406c2f23c461d66485e54bca8

View on Chainz ↗

Height

#710,636

Difficulty

10.956335

Transactions

Size

699 B

Version

Bits

0af4d262

Nonce

217,656

Timestamp

9/7/2014, 7:32:37 AM

Confirmations

6,083,610

Merkle Root

444276e172b453850a35153b8212540b7508d9fa26da38c9c79eb8793be58b98

Transactions (1)

Coinbase444276e172b453…9eb8793be58b98

1 in → 16 out8.3200 XPM607 B

AXz2kWvX…V5ZFCDBd AJzWx2VD…j4ZSMit5 APfZjrNu…Wvzt6AFp APZ75aGq…cWXbE4rY AebWhrRm…K61Qrkws

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.

1.712 × 10⁹⁹(100-digit number)

17125665931349798838…79761594894062003199

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

1.712 × 10⁹⁹(100-digit number)

17125665931349798838…79761594894062003199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.712 × 10⁹⁹(100-digit number)

17125665931349798838…79761594894062003201

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

3.425 × 10⁹⁹(100-digit number)

34251331862699597677…59523189788124006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.425 × 10⁹⁹(100-digit number)

34251331862699597677…59523189788124006401

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

6.850 × 10⁹⁹(100-digit number)

68502663725399195355…19046379576248012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.850 × 10⁹⁹(100-digit number)

68502663725399195355…19046379576248012801

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

1.370 × 10¹⁰⁰(101-digit number)

13700532745079839071…38092759152496025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.370 × 10¹⁰⁰(101-digit number)

13700532745079839071…38092759152496025601

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

2.740 × 10¹⁰⁰(101-digit number)

27401065490159678142…76185518304992051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.740 × 10¹⁰⁰(101-digit number)

27401065490159678142…76185518304992051201

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