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Block #144,086

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/1/2013, 2:32:29 AM Β· Difficulty 9.8377 Β· 6,650,962 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a2a04cda93cfe0cf997c65ecee33be20838091b506663bfe7c478aed5feaf75d
View on Chainz β†—

Height

#144,086

Difficulty

9.837731

Transactions

2

Size

5.97 KB

Version

2

Bits

09d67582

Nonce

602,657

Timestamp

9/1/2013, 2:32:29 AM

Confirmations

6,650,962

Mined by

⛏️ P2SHAMuPUQM2C7rLqSuu1zthpFL5zWn4be3qjy

Merkle Root

98b547ceeb5dee2c6ee70ebbbe9a7e71ec14f4c488670c3c0ebb53422ebb073b
Transactions (2)
Coinbased0a3c385f8c025…b3068b08b00c12
1 in β†’ 1 out10.3871 XPM109 B
AMuPUQM2…n4be3qjy
ac429435af1dc5…6248821758c10e
50 in β†’ 1 out466.3200 XPM5.78 KB
ATWpCFic…6AT1WprT
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.

1.043 Γ— 10⁹⁹(100-digit number)
10437482105613461808…63160535728509049839
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
1.043 Γ— 10⁹⁹(100-digit number)
10437482105613461808…63160535728509049839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.043 Γ— 10⁹⁹(100-digit number)
10437482105613461808…63160535728509049841
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
2.087 Γ— 10⁹⁹(100-digit number)
20874964211226923616…26321071457018099679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.087 Γ— 10⁹⁹(100-digit number)
20874964211226923616…26321071457018099681
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
4.174 Γ— 10⁹⁹(100-digit number)
41749928422453847232…52642142914036199359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.174 Γ— 10⁹⁹(100-digit number)
41749928422453847232…52642142914036199361
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
8.349 Γ— 10⁹⁹(100-digit number)
83499856844907694465…05284285828072398719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.349 Γ— 10⁹⁹(100-digit number)
83499856844907694465…05284285828072398721
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
1.669 Γ— 10¹⁰⁰(101-digit number)
16699971368981538893…10568571656144797439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,604,424 XPMΒ·at block #6,795,047 Β· updates every 60s
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