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Block #161,441

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 4:15:45 PM Β· Difficulty 9.8593 Β· 6,650,931 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b8b5db8c52ad129144919250a478b050ef4085ab7e1dcef4c07b480dcdc5a0aa
View on Chainz β†—

Height

#161,441

Difficulty

9.859306

Transactions

2

Size

503 B

Version

2

Bits

09dbfb78

Nonce

141,807

Timestamp

9/12/2013, 4:15:45 PM

Confirmations

6,650,931

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

6ae5413ec4da8826653f5a2fc3981988f82cdecf09a185f8ec02b45d92cb0523
Transactions (2)
Coinbase78b4ece0a64dbc…c72c3d6b1d8c0d
1 in β†’ 1 out10.2800 XPM109 B
AYkoKAQ4…uuj8DeZs
158d934a47ce2d…7e73dd5ae87e28
2 in β†’ 2 out20.5200 XPM305 B
AFz9fXym…wh4UqpkLAPfE79Vf…Ax3MXEDN
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.

2.007 Γ— 10⁹³(94-digit number)
20078505687131816184…66421675950582270399
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
2.007 Γ— 10⁹³(94-digit number)
20078505687131816184…66421675950582270399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.007 Γ— 10⁹³(94-digit number)
20078505687131816184…66421675950582270401
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
4.015 Γ— 10⁹³(94-digit number)
40157011374263632369…32843351901164540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.015 Γ— 10⁹³(94-digit number)
40157011374263632369…32843351901164540801
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
8.031 Γ— 10⁹³(94-digit number)
80314022748527264738…65686703802329081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.031 Γ— 10⁹³(94-digit number)
80314022748527264738…65686703802329081601
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
1.606 Γ— 10⁹⁴(95-digit number)
16062804549705452947…31373407604658163199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.606 Γ— 10⁹⁴(95-digit number)
16062804549705452947…31373407604658163201
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
3.212 Γ— 10⁹⁴(95-digit number)
32125609099410905895…62746815209316326399
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:57,742,997 XPMΒ·at block #6,812,371 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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