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Block #281,264

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2013, 11:24:31 PM Β· Difficulty 9.9766 Β· 6,528,645 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c2ae42e747275b5f14db84b83ec0aeb2b97409de4dd3dae13b16d4021f1eb56a
View on Chainz β†—

Height

#281,264

Difficulty

9.976587

Transactions

2

Size

1.43 KB

Version

2

Bits

09fa01a3

Nonce

94,065

Timestamp

11/28/2013, 11:24:31 PM

Confirmations

6,528,645

Mined by

⛏️ P2SHAaV9ckuEmbgdVe2cgWm5A4oENPfkxBtyk6

Merkle Root

4f9bd373fd279bdb5aec9a75952584761e49ffcd0947c821892d6505e55c1b0b
Transactions (2)
Coinbase4ba1ff725087d3…0ab2feee37274b
1 in β†’ 1 out10.0500 XPM109 B
AaV9ckuE…fkxBtyk6
6fae3e52be0289…5019cc994c6688
8 in β†’ 2 out2.0101 XPM1.23 KB
ANxMPRii…2tx37K4gAavnhQb4…YUuhuXjU
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.

4.125 Γ— 10⁹⁴(95-digit number)
41250185198381749938…49398342913759265199
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
4.125 Γ— 10⁹⁴(95-digit number)
41250185198381749938…49398342913759265199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.125 Γ— 10⁹⁴(95-digit number)
41250185198381749938…49398342913759265201
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
8.250 Γ— 10⁹⁴(95-digit number)
82500370396763499876…98796685827518530399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.250 Γ— 10⁹⁴(95-digit number)
82500370396763499876…98796685827518530401
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
1.650 Γ— 10⁹⁡(96-digit number)
16500074079352699975…97593371655037060799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.650 Γ— 10⁹⁡(96-digit number)
16500074079352699975…97593371655037060801
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
3.300 Γ— 10⁹⁡(96-digit number)
33000148158705399950…95186743310074121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.300 Γ— 10⁹⁡(96-digit number)
33000148158705399950…95186743310074121601
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
6.600 Γ— 10⁹⁡(96-digit number)
66000296317410799901…90373486620148243199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.600 Γ— 10⁹⁡(96-digit number)
66000296317410799901…90373486620148243201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,723,355 XPMΒ·at block #6,809,908 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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