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Block #170,008

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2013, 10:46:07 AM Β· Difficulty 9.8666 Β· 6,636,469 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b2206b8f41cca5c43405d8b3ace21c8adc49f78af1fb097f6669513271ced66
View on Chainz β†—

Height

#170,008

Difficulty

9.866644

Transactions

1

Size

198 B

Version

2

Bits

09dddc61

Nonce

5,428

Timestamp

9/18/2013, 10:46:07 AM

Confirmations

6,636,469

Mined by

⛏️ P2SHAP1gyZXxfrBjGDz3MkjK6fwMgGuWqJpvNn

Merkle Root

cb14e1cdd44411c98d6ca8eb4ab4c4014e3a608ef3bb97908f3da417ad93d634
Transactions (1)
Coinbasecb14e1cdd44411…3da417ad93d634
1 in β†’ 1 out10.2600 XPM109 B
AP1gyZXx…uWqJpvNn
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.

6.424 Γ— 10⁹²(93-digit number)
64241739048178399832…73744702431202943999
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
6.424 Γ— 10⁹²(93-digit number)
64241739048178399832…73744702431202943999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.424 Γ— 10⁹²(93-digit number)
64241739048178399832…73744702431202944001
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
1.284 Γ— 10⁹³(94-digit number)
12848347809635679966…47489404862405887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.284 Γ— 10⁹³(94-digit number)
12848347809635679966…47489404862405888001
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
2.569 Γ— 10⁹³(94-digit number)
25696695619271359932…94978809724811775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.569 Γ— 10⁹³(94-digit number)
25696695619271359932…94978809724811776001
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
5.139 Γ— 10⁹³(94-digit number)
51393391238542719865…89957619449623551999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.139 Γ— 10⁹³(94-digit number)
51393391238542719865…89957619449623552001
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
1.027 Γ— 10⁹⁴(95-digit number)
10278678247708543973…79915238899247103999
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:57,695,908 XPMΒ·at block #6,806,476 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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