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Block #262,438

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2013, 8:47:17 PM Β· Difficulty 9.9686 Β· 6,542,528 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
accc88ea5a3f0b1dc4654fd7248dec280e65ae9b7247a6712fa8e5338839f4de
View on Chainz β†—

Height

#262,438

Difficulty

9.968600

Transactions

2

Size

394 B

Version

2

Bits

09f7f626

Nonce

31,682

Timestamp

11/16/2013, 8:47:17 PM

Confirmations

6,542,528

Mined by

⛏️ P2SHAGh8uc6ZPLAE78AHhCyNsvpSvTd6ZjSBQJ

Merkle Root

5ace107666b221d11e561cd9aca41056bfc11f82cb5c8a731374201da514defd
Transactions (2)
Coinbase88262678eda0de…a063d82c043ba8
1 in β†’ 1 out10.0600 XPM109 B
AGh8uc6Z…d6ZjSBQJ
22eb06cd763d62…28e74820554611
1 in β†’ 2 out10.0300 XPM193 B
AXX9rz27…X689a2UVAVZvNLFL…qcJM8HJV
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.

2.454 Γ— 10⁹⁹(100-digit number)
24548199621727347757…97758839460179425279
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
2.454 Γ— 10⁹⁹(100-digit number)
24548199621727347757…97758839460179425279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.454 Γ— 10⁹⁹(100-digit number)
24548199621727347757…97758839460179425281
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
4.909 Γ— 10⁹⁹(100-digit number)
49096399243454695514…95517678920358850559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.909 Γ— 10⁹⁹(100-digit number)
49096399243454695514…95517678920358850561
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
9.819 Γ— 10⁹⁹(100-digit number)
98192798486909391029…91035357840717701119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.819 Γ— 10⁹⁹(100-digit number)
98192798486909391029…91035357840717701121
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
1.963 Γ— 10¹⁰⁰(101-digit number)
19638559697381878205…82070715681435402239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.963 Γ— 10¹⁰⁰(101-digit number)
19638559697381878205…82070715681435402241
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
3.927 Γ— 10¹⁰⁰(101-digit number)
39277119394763756411…64141431362870804479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.927 Γ— 10¹⁰⁰(101-digit number)
39277119394763756411…64141431362870804481
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:57,683,795 XPMΒ·at block #6,804,965 Β· updates every 60s
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