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Block #144,505

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2013, 8:40:57 AM Β· Difficulty 9.8394 Β· 6,672,562 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a4346be4f733de8f795786a7cc38e81b45b790191df6a5991523dbe728bdad9
View on Chainz β†—

Height

#144,505

Difficulty

9.839388

Transactions

2

Size

3.64 KB

Version

2

Bits

09d6e228

Nonce

70,670

Timestamp

9/1/2013, 8:40:57 AM

Confirmations

6,672,562

Mined by

⛏️ P2SHAZUG6xBqU5fxPGco3jfkcMFpPpsAUu2ZCu

Merkle Root

ed754cb3590601e45c3ba87480567701768ae4a4d5fa55e7ff7e65960156ddd4
Transactions (2)
Coinbase014cf7f2daf37b…0dee7c9c0376fc
1 in β†’ 1 out10.3500 XPM109 B
AZUG6xBq…sAUu2ZCu
4d9204c8af6523…49d07555360268
29 in β†’ 1 out314.4891 XPM3.44 KB
AScCYXya…oAz38X3p
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.

2.775 Γ— 10⁹⁢(97-digit number)
27754853522913336952…32359949512175203199
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
2.775 Γ— 10⁹⁢(97-digit number)
27754853522913336952…32359949512175203199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.775 Γ— 10⁹⁢(97-digit number)
27754853522913336952…32359949512175203201
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
5.550 Γ— 10⁹⁢(97-digit number)
55509707045826673905…64719899024350406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.550 Γ— 10⁹⁢(97-digit number)
55509707045826673905…64719899024350406401
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
1.110 Γ— 10⁹⁷(98-digit number)
11101941409165334781…29439798048700812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.110 Γ— 10⁹⁷(98-digit number)
11101941409165334781…29439798048700812801
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
2.220 Γ— 10⁹⁷(98-digit number)
22203882818330669562…58879596097401625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.220 Γ— 10⁹⁷(98-digit number)
22203882818330669562…58879596097401625601
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
4.440 Γ— 10⁹⁷(98-digit number)
44407765636661339124…17759192194803251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.440 Γ— 10⁹⁷(98-digit number)
44407765636661339124…17759192194803251201
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:57,780,571 XPMΒ·at block #6,817,066 Β· updates every 60s
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