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Block #41,873

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 5:27:28 PM Β· Difficulty 8.5597 Β· 6,765,261 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98938f8ceecbb65ba12a7889843649dd16307c24dc27a615d7adcfe004419197
View on Chainz β†—

Height

#41,873

Difficulty

8.559669

Transactions

1

Size

199 B

Version

2

Bits

088f467f

Nonce

800

Timestamp

7/14/2013, 5:27:28 PM

Confirmations

6,765,261

Mined by

⛏️ P2SHAcjhaVoWPPShdSp4K3fBKNtTx1hAPjZTBV

Merkle Root

f9c4bd321f12df239f55f803578f89c9f45991c55be10dc07b778515e8d1d8af
Transactions (1)
Coinbasef9c4bd321f12df…778515e8d1d8af
1 in β†’ 1 out13.6300 XPM110 B
AcjhaVoW…hAPjZTBV
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.

3.664 Γ— 10⁹³(94-digit number)
36647618851642680283…97048511694463585459
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
3.664 Γ— 10⁹³(94-digit number)
36647618851642680283…97048511694463585459
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.664 Γ— 10⁹³(94-digit number)
36647618851642680283…97048511694463585461
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
7.329 Γ— 10⁹³(94-digit number)
73295237703285360566…94097023388927170919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.329 Γ— 10⁹³(94-digit number)
73295237703285360566…94097023388927170921
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
1.465 Γ— 10⁹⁴(95-digit number)
14659047540657072113…88194046777854341839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.465 Γ— 10⁹⁴(95-digit number)
14659047540657072113…88194046777854341841
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
2.931 Γ— 10⁹⁴(95-digit number)
29318095081314144226…76388093555708683679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.931 Γ— 10⁹⁴(95-digit number)
29318095081314144226…76388093555708683681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,701,177 XPMΒ·at block #6,807,133 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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