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Block #254,342

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/10/2013, 4:20:21 PM Β· Difficulty 9.9730 Β· 6,542,470 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0afa8af35f07726a71e9fcb12482a9083734906bfacac92a5b3ccfa61a92c595
View on Chainz β†—

Height

#254,342

Difficulty

9.972987

Transactions

2

Size

423 B

Version

2

Bits

09f915b5

Nonce

28,501

Timestamp

11/10/2013, 4:20:21 PM

Confirmations

6,542,470

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

993d2fdcaaf0525c96a797f41a715a9db66472f2ac5ad4bc4d00ba254efd2657
Transactions (2)
Coinbasee9a475d930d83f…07d7ae1dcde4f6
1 in β†’ 2 out10.0500 XPM141 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
28097584d979ce…98d233645ab02a
1 in β†’ 1 out9.9900 XPM192 B
AJtCDakk…cmy9cKRa
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.

3.509 Γ— 10⁹⁴(95-digit number)
35096994693757677392…91963972524915752339
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
3.509 Γ— 10⁹⁴(95-digit number)
35096994693757677392…91963972524915752339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.509 Γ— 10⁹⁴(95-digit number)
35096994693757677392…91963972524915752341
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
7.019 Γ— 10⁹⁴(95-digit number)
70193989387515354784…83927945049831504679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.019 Γ— 10⁹⁴(95-digit number)
70193989387515354784…83927945049831504681
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
1.403 Γ— 10⁹⁡(96-digit number)
14038797877503070956…67855890099663009359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.403 Γ— 10⁹⁡(96-digit number)
14038797877503070956…67855890099663009361
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
2.807 Γ— 10⁹⁡(96-digit number)
28077595755006141913…35711780199326018719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.807 Γ— 10⁹⁡(96-digit number)
28077595755006141913…35711780199326018721
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
5.615 Γ— 10⁹⁡(96-digit number)
56155191510012283827…71423560398652037439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.615 Γ— 10⁹⁡(96-digit number)
56155191510012283827…71423560398652037441
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:57,618,511 XPMΒ·at block #6,796,811 Β· updates every 60s
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