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Block #168,710

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2013, 12:07:59 PM Β· Difficulty 9.8681 Β· 6,627,822 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f0692ab94553e5b5edc48ec451ba346321d8667f41023b544081bf2ef2273c9b
View on Chainz β†—

Height

#168,710

Difficulty

9.868149

Transactions

1

Size

198 B

Version

2

Bits

09de3f04

Nonce

14,699

Timestamp

9/17/2013, 12:07:59 PM

Confirmations

6,627,822

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

a6aea5002cbd2c21b8eb985291b5d4ceddf44bbce8bc8e3548d8da4b6cbb1370
Transactions (1)
Coinbasea6aea5002cbd2c…d8da4b6cbb1370
1 in β†’ 1 out10.2500 XPM109 B
AYc3QGYa…SWDuszQp
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.

5.396 Γ— 10⁹²(93-digit number)
53969271203074766435…02927971320938379769
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
5.396 Γ— 10⁹²(93-digit number)
53969271203074766435…02927971320938379769
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.396 Γ— 10⁹²(93-digit number)
53969271203074766435…02927971320938379771
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
1.079 Γ— 10⁹³(94-digit number)
10793854240614953287…05855942641876759539
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.079 Γ— 10⁹³(94-digit number)
10793854240614953287…05855942641876759541
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
2.158 Γ— 10⁹³(94-digit number)
21587708481229906574…11711885283753519079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.158 Γ— 10⁹³(94-digit number)
21587708481229906574…11711885283753519081
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
4.317 Γ— 10⁹³(94-digit number)
43175416962459813148…23423770567507038159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.317 Γ— 10⁹³(94-digit number)
43175416962459813148…23423770567507038161
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
8.635 Γ— 10⁹³(94-digit number)
86350833924919626296…46847541135014076319
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:57,616,252 XPMΒ·at block #6,796,531 Β· updates every 60s
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