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Block #1,534,695

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 10:07:57 AM Β· Difficulty 10.6178 Β· 5,279,432 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
99f9e26f2d5cb21d80f76c69567a30fda0d1e16c028954080c962e7aef6dd608
View on Chainz β†—

Height

#1,534,695

Difficulty

10.617803

Transactions

2

Size

7.62 KB

Version

2

Bits

0a9e285a

Nonce

212,644,479

Timestamp

4/10/2016, 10:07:57 AM

Confirmations

5,279,432

Mined by

⛏️ P2SHAWuWytnrtKq6hrn1hAjcB1NsJap9xWVQXn

Merkle Root

9868d3f7a63f6211943e1919cc59bf1b77ec22c1aecfdff274fe69d70288da39
Transactions (2)
Coinbasedc417da807004d…1bdcff26d3e44a
1 in β†’ 1 out8.9400 XPM109 B
AWuWytnr…p9xWVQXn
aca88cc6d05ae2…7fc707662d90be
51 in β†’ 1 out1394.4781 XPM7.42 KB
ANPyk9fx…frVXSMKX
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.

1.020 Γ— 10⁹⁴(95-digit number)
10209568670946201334…11960776070421617359
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
1.020 Γ— 10⁹⁴(95-digit number)
10209568670946201334…11960776070421617359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.020 Γ— 10⁹⁴(95-digit number)
10209568670946201334…11960776070421617361
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
2.041 Γ— 10⁹⁴(95-digit number)
20419137341892402669…23921552140843234719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.041 Γ— 10⁹⁴(95-digit number)
20419137341892402669…23921552140843234721
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
4.083 Γ— 10⁹⁴(95-digit number)
40838274683784805339…47843104281686469439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.083 Γ— 10⁹⁴(95-digit number)
40838274683784805339…47843104281686469441
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
8.167 Γ— 10⁹⁴(95-digit number)
81676549367569610679…95686208563372938879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.167 Γ— 10⁹⁴(95-digit number)
81676549367569610679…95686208563372938881
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
1.633 Γ— 10⁹⁡(96-digit number)
16335309873513922135…91372417126745877759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.633 Γ— 10⁹⁡(96-digit number)
16335309873513922135…91372417126745877761
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:57,757,101 XPMΒ·at block #6,814,126 Β· updates every 60s
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