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Block #246,666

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/6/2013, 7:14:27 AM Β· Difficulty 9.9642 Β· 6,559,781 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2393625c5c33154fd7018bd3afbbb894bca2735044a9ca032436ace37a9c3982
View on Chainz β†—

Height

#246,666

Difficulty

9.964243

Transactions

2

Size

1.14 KB

Version

2

Bits

09f6d89f

Nonce

40,632

Timestamp

11/6/2013, 7:14:27 AM

Confirmations

6,559,781

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

141107f742eba6020a7212254508193ce1beaff81f9e0acb1b5a5f299e0b2df8
Transactions (2)
Coinbasefab2d828dc7455…98bd4fd50bdfaa
1 in β†’ 2 out10.0700 XPM142 B
AKcbk49N…GJbKa7j1ASNt3cJa…L5zCqAYM
0f4b690a9ce49d…8e2569a15c442e
6 in β†’ 1 out98.9900 XPM932 B
AHUbt4Ww…hcxVK8Cp
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.

3.356 Γ— 10⁹⁡(96-digit number)
33566795884472552114…46352088077990207999
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
3.356 Γ— 10⁹⁡(96-digit number)
33566795884472552114…46352088077990207999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.356 Γ— 10⁹⁡(96-digit number)
33566795884472552114…46352088077990208001
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
6.713 Γ— 10⁹⁡(96-digit number)
67133591768945104229…92704176155980415999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.713 Γ— 10⁹⁡(96-digit number)
67133591768945104229…92704176155980416001
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
1.342 Γ— 10⁹⁢(97-digit number)
13426718353789020845…85408352311960831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.342 Γ— 10⁹⁢(97-digit number)
13426718353789020845…85408352311960832001
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
2.685 Γ— 10⁹⁢(97-digit number)
26853436707578041691…70816704623921663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.685 Γ— 10⁹⁢(97-digit number)
26853436707578041691…70816704623921664001
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
5.370 Γ— 10⁹⁢(97-digit number)
53706873415156083383…41633409247843327999
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:57,695,665 XPMΒ·at block #6,806,446 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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