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Block #249,241

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2013, 8:25:23 PM Β· Difficulty 9.9667 Β· 6,564,971 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1630bd89182cc620928ed1fd0476d964f2c79a7ca0d278ddb66413bfbe26cf88
View on Chainz β†—

Height

#249,241

Difficulty

9.966700

Transactions

2

Size

425 B

Version

2

Bits

09f779a8

Nonce

18,385

Timestamp

11/7/2013, 8:25:23 PM

Confirmations

6,564,971

Mined by

⛏️ P2SHAG76bAu9WTbVtqD7wh8Uu7LAq9tcsVSM1r

Merkle Root

d85d705410537ebbef037cbef8028852d0841b7dcb206698c1c3c791dafa7e32
Transactions (2)
Coinbasefe4b0db74a7027…57ad8240cac43a
1 in β†’ 1 out10.0600 XPM109 B
AG76bAu9…tcsVSM1r
a13e11c7acc77a…4bdea561537cb8
1 in β†’ 2 out98.4223 XPM226 B
AUX8XVLy…tV4vR9KBAZdmkNt9…Dk8ffFeU
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.

5.310 Γ— 10⁹³(94-digit number)
53108377188167364536…45953485014630994319
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
5.310 Γ— 10⁹³(94-digit number)
53108377188167364536…45953485014630994319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.310 Γ— 10⁹³(94-digit number)
53108377188167364536…45953485014630994321
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
1.062 Γ— 10⁹⁴(95-digit number)
10621675437633472907…91906970029261988639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.062 Γ— 10⁹⁴(95-digit number)
10621675437633472907…91906970029261988641
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
2.124 Γ— 10⁹⁴(95-digit number)
21243350875266945814…83813940058523977279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.124 Γ— 10⁹⁴(95-digit number)
21243350875266945814…83813940058523977281
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
4.248 Γ— 10⁹⁴(95-digit number)
42486701750533891629…67627880117047954559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.248 Γ— 10⁹⁴(95-digit number)
42486701750533891629…67627880117047954561
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
8.497 Γ— 10⁹⁴(95-digit number)
84973403501067783258…35255760234095909119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.497 Γ— 10⁹⁴(95-digit number)
84973403501067783258…35255760234095909121
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:57,757,764 XPMΒ·at block #6,814,211 Β· updates every 60s
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