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Block #571,005

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2014, 5:14:34 AM Β· Difficulty 10.9650 Β· 6,234,976 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3c04463b26289862bbc89c0d674d0ed0ed2a36e6745cac24753577e92d9f6dc2
View on Chainz β†—

Height

#571,005

Difficulty

10.964992

Transactions

4

Size

1.30 KB

Version

2

Bits

0af709bb

Nonce

392,463,161

Timestamp

6/1/2014, 5:14:34 AM

Confirmations

6,234,976

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

900d20be684486585e9d43e2519a06efb6c498214f2379f2484147fe78f82145
Transactions (4)
Coinbase44b2ff378d7b94…4c07d11bf737f4
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
ef222405f8ade4…1a699dc28e6fe8
3 in β†’ 2 out329.2501 XPM523 B
Ae6wdd2V…yV8UfJLLAHHUEXa6…qnZc6FkA
d027cf776b32c1…d564fe52d09291
2 in β†’ 2 out11.0201 XPM373 B
AXg13KSy…KcbKvCfQAWAbb2pL…4Wmht5QK
ad6f0f6d439d24…2a21da9227c3fe
1 in β†’ 2 out6.4687 XPM226 B
AM23VEk3…q622MtoHAUtKbZa1…UbB15aYP
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.

7.088 Γ— 10⁹⁢(97-digit number)
70882994270254905348…03414192592877313349
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
7.088 Γ— 10⁹⁢(97-digit number)
70882994270254905348…03414192592877313349
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.088 Γ— 10⁹⁢(97-digit number)
70882994270254905348…03414192592877313351
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
1.417 Γ— 10⁹⁷(98-digit number)
14176598854050981069…06828385185754626699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.417 Γ— 10⁹⁷(98-digit number)
14176598854050981069…06828385185754626701
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
2.835 Γ— 10⁹⁷(98-digit number)
28353197708101962139…13656770371509253399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.835 Γ— 10⁹⁷(98-digit number)
28353197708101962139…13656770371509253401
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
5.670 Γ— 10⁹⁷(98-digit number)
56706395416203924278…27313540743018506799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.670 Γ— 10⁹⁷(98-digit number)
56706395416203924278…27313540743018506801
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
1.134 Γ— 10⁹⁸(99-digit number)
11341279083240784855…54627081486037013599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.134 Γ— 10⁹⁸(99-digit number)
11341279083240784855…54627081486037013601
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:57,691,924 XPMΒ·at block #6,805,980 Β· updates every 60s
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