Block #1,177,306

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/30/2015, 6:02:15 PM · Difficulty 10.9361 · 5,649,776 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cff3f3adee07ebd234facab7179bfb2188b70aa5d741f385174a781d099332c0

View on Chainz ↗

Height

#1,177,306

Difficulty

10.936061

Transactions

Size

1.50 KB

Version

Bits

0aefa1b6

Nonce

11,405,352

Timestamp

7/30/2015, 6:02:15 PM

Confirmations

5,649,776

Mined by

⛏️ P2SHAUHn2ZVa7iNVVEttpiqxkepoR9bSXJTMKR

Merkle Root

ac7e6ce144124eaaeb9e4f09810e70da09c4b66bd2d6aad2790b71c585e291f0

Transactions (3)

Coinbase75d51e90009bed…2ba917a16e9e69

1 in → 1 out8.3900 XPM109 B

AUHn2ZVa…bSXJTMKR

f482e6b6cadb66…ef295954556423

1 in → 2 out999.9800 XPM225 B

AJjnK9uC…VreFquR4 ANYkZniv…XNZhv4cN

a16bc025f5b115…21c3bc6a732a31

7 in → 2 out60.1705 XPM1.09 KB

Adjv62kq…8Pyb2qJ3 AK9LxQQh…h24pctRm

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.

2.042 × 10⁹⁴(95-digit number)

20421561821934498440…45809458182144942079

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

2.042 × 10⁹⁴(95-digit number)

20421561821934498440…45809458182144942079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.042 × 10⁹⁴(95-digit number)

20421561821934498440…45809458182144942081

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

4.084 × 10⁹⁴(95-digit number)

40843123643868996881…91618916364289884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.084 × 10⁹⁴(95-digit number)

40843123643868996881…91618916364289884161

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

8.168 × 10⁹⁴(95-digit number)

81686247287737993763…83237832728579768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.168 × 10⁹⁴(95-digit number)

81686247287737993763…83237832728579768321

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

1.633 × 10⁹⁵(96-digit number)

16337249457547598752…66475665457159536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.633 × 10⁹⁵(96-digit number)

16337249457547598752…66475665457159536641

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

3.267 × 10⁹⁵(96-digit number)

32674498915095197505…32951330914319073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.267 × 10⁹⁵(96-digit number)

32674498915095197505…32951330914319073281

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

6.534 × 10⁹⁵(96-digit number)

65348997830190395010…65902661828638146559

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 #1,177,306

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