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Block #162,865

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 2:42:10 PM Β· Difficulty 9.8615 Β· 6,633,806 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b44b1250e99935645b066275dae51f2b5264f43faf5dc5c2691d7749e6896fa4
View on Chainz β†—

Height

#162,865

Difficulty

9.861490

Transactions

2

Size

358 B

Version

2

Bits

09dc8a9a

Nonce

104,059

Timestamp

9/13/2013, 2:42:10 PM

Confirmations

6,633,806

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

ec7298cd93e7407cea342d17d713b2241a5dae96f2e9b91874b30647b87567ea
Transactions (2)
Coinbase563057c137d23e…856862e07b41f0
1 in β†’ 1 out10.2800 XPM109 B
AX99MLNm…vtidqEwE
2a166797b68a85…9c7a6af3adf1af
1 in β†’ 1 out10.2500 XPM159 B
APug1zqH…wfikf34c
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.

3.078 Γ— 10⁹⁡(96-digit number)
30782393556434360664…36458645087973978919
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
3.078 Γ— 10⁹⁡(96-digit number)
30782393556434360664…36458645087973978919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.078 Γ— 10⁹⁡(96-digit number)
30782393556434360664…36458645087973978921
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
6.156 Γ— 10⁹⁡(96-digit number)
61564787112868721329…72917290175947957839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.156 Γ— 10⁹⁡(96-digit number)
61564787112868721329…72917290175947957841
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
1.231 Γ— 10⁹⁢(97-digit number)
12312957422573744265…45834580351895915679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.231 Γ— 10⁹⁢(97-digit number)
12312957422573744265…45834580351895915681
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
2.462 Γ— 10⁹⁢(97-digit number)
24625914845147488531…91669160703791831359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.462 Γ— 10⁹⁢(97-digit number)
24625914845147488531…91669160703791831361
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
4.925 Γ— 10⁹⁢(97-digit number)
49251829690294977063…83338321407583662719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.925 Γ— 10⁹⁢(97-digit number)
49251829690294977063…83338321407583662721
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:57,617,372 XPMΒ·at block #6,796,670 Β· updates every 60s
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