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Block #1,073,278

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2015, 6:28:47 AM Β· Difficulty 10.7415 Β· 5,721,742 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
26ca61c32fb06bc5127efb287cf6170d5f287ddab155b9e2db30f308d7e7b145
View on Chainz β†—

Height

#1,073,278

Difficulty

10.741508

Transactions

2

Size

572 B

Version

2

Bits

0abdd37e

Nonce

1,608,879,788

Timestamp

5/24/2015, 6:28:47 AM

Confirmations

5,721,742

Mined by

⛏️ P2SHAY8QXh7yF7wWMBLqD5McTJFicxBgkUetEG

Merkle Root

06cbbeae1c986b7f82d8f0211d774d3c7cd3d07740fe81b13ed8c62dd7da8a67
Transactions (2)
Coinbase1d63612fee07a6…22aedd77259cf1
1 in β†’ 1 out8.6600 XPM109 B
AY8QXh7y…BgkUetEG
95cae1296a93da…6d503330103976
2 in β†’ 2 out12.6197 XPM373 B
Ae9drWdk…FnLTm9PnAPhgdts9…U7cZ9YKj
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.

9.653 Γ— 10⁹³(94-digit number)
96537570520621129743…28864999314543581959
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
9.653 Γ— 10⁹³(94-digit number)
96537570520621129743…28864999314543581959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.653 Γ— 10⁹³(94-digit number)
96537570520621129743…28864999314543581961
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
1.930 Γ— 10⁹⁴(95-digit number)
19307514104124225948…57729998629087163919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.930 Γ— 10⁹⁴(95-digit number)
19307514104124225948…57729998629087163921
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
3.861 Γ— 10⁹⁴(95-digit number)
38615028208248451897…15459997258174327839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.861 Γ— 10⁹⁴(95-digit number)
38615028208248451897…15459997258174327841
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
7.723 Γ— 10⁹⁴(95-digit number)
77230056416496903794…30919994516348655679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.723 Γ— 10⁹⁴(95-digit number)
77230056416496903794…30919994516348655681
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
1.544 Γ— 10⁹⁡(96-digit number)
15446011283299380758…61839989032697311359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.544 Γ— 10⁹⁡(96-digit number)
15446011283299380758…61839989032697311361
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:57,604,206 XPMΒ·at block #6,795,019 Β· updates every 60s
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