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Block #168,967

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2013, 4:17:09 PM Β· Difficulty 9.8684 Β· 6,642,090 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
356fedf76a963e173a5e9446e05efdac3f53e2308cbd0241e7b64e090837fd9d
View on Chainz β†—

Height

#168,967

Difficulty

9.868364

Transactions

1

Size

198 B

Version

2

Bits

09de4d1b

Nonce

60,443

Timestamp

9/17/2013, 4:17:09 PM

Confirmations

6,642,090

Mined by

⛏️ P2SHAZz6Bg87J8VhAYyRKDwNgf7vf5MZtiQn8U

Merkle Root

a062e4cc1f612dae76b221bfe9e30c0db8106e9eb9f2711f568f5a1be92a2721
Transactions (1)
Coinbasea062e4cc1f612d…8f5a1be92a2721
1 in β†’ 1 out10.2500 XPM109 B
AZz6Bg87…MZtiQn8U
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.662 Γ— 10⁹²(93-digit number)
76624715471470960570…28508213416928039679
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.662 Γ— 10⁹²(93-digit number)
76624715471470960570…28508213416928039679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.662 Γ— 10⁹²(93-digit number)
76624715471470960570…28508213416928039681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.532 Γ— 10⁹³(94-digit number)
15324943094294192114…57016426833856079359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.532 Γ— 10⁹³(94-digit number)
15324943094294192114…57016426833856079361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.064 Γ— 10⁹³(94-digit number)
30649886188588384228…14032853667712158719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.064 Γ— 10⁹³(94-digit number)
30649886188588384228…14032853667712158721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.129 Γ— 10⁹³(94-digit number)
61299772377176768456…28065707335424317439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.129 Γ— 10⁹³(94-digit number)
61299772377176768456…28065707335424317441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.225 Γ— 10⁹⁴(95-digit number)
12259954475435353691…56131414670848634879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,732,560 XPMΒ·at block #6,811,056 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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