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Block #65,085

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 10:35:40 AM Β· Difficulty 8.9833 Β· 6,747,205 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7814109fdec373033cd084926141c5ac0d9a238688debef152979321b2bb6c55
View on Chainz β†—

Height

#65,085

Difficulty

8.983302

Transactions

1

Size

201 B

Version

2

Bits

08fbb9a7

Nonce

671

Timestamp

7/19/2013, 10:35:40 AM

Confirmations

6,747,205

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

3b31962e438bd9d31b126decab1ab343b99f3de651d26cf7ddf9a9b18d7ca77d
Transactions (1)
Coinbase3b31962e438bd9…f9a9b18d7ca77d
1 in β†’ 1 out12.3700 XPM110 B
AJbz55M2…moHxsz79
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.

9.817 Γ— 10⁹⁷(98-digit number)
98170153436506300720…81021532419080249969
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
9.817 Γ— 10⁹⁷(98-digit number)
98170153436506300720…81021532419080249969
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.817 Γ— 10⁹⁷(98-digit number)
98170153436506300720…81021532419080249971
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
1.963 Γ— 10⁹⁸(99-digit number)
19634030687301260144…62043064838160499939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.963 Γ— 10⁹⁸(99-digit number)
19634030687301260144…62043064838160499941
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
3.926 Γ— 10⁹⁸(99-digit number)
39268061374602520288…24086129676320999879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.926 Γ— 10⁹⁸(99-digit number)
39268061374602520288…24086129676320999881
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
7.853 Γ— 10⁹⁸(99-digit number)
78536122749205040576…48172259352641999759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.853 Γ— 10⁹⁸(99-digit number)
78536122749205040576…48172259352641999761
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
1.570 Γ— 10⁹⁹(100-digit number)
15707224549841008115…96344518705283999519
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:57,742,339 XPMΒ·at block #6,812,289 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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