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Block #2,151,817

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2017, 3:38:34 PM Β· Difficulty 10.9003 Β· 4,658,091 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8bfd321f4be9d578193cfb2a7d2d8fe6debdca1a87815dccf43fa8775c3ba8f2
View on Chainz β†—

Height

#2,151,817

Difficulty

10.900267

Transactions

2

Size

2.12 KB

Version

2

Bits

0ae677df

Nonce

628,914,037

Timestamp

6/8/2017, 3:38:34 PM

Confirmations

4,658,091

Mined by

⛏️ P2SHAHTmEUVzNUAwLcvSi14Ta4NTBpWk5E8Ssp

Merkle Root

5b5159ff607f8ea6e8d66c92ad107f4344b37dc0be76372e6c7d9c12828bd837
Transactions (2)
Coinbase5c0ccab7cc8c6f…88f78e91f87a7f
1 in β†’ 1 out8.4600 XPM110 B
AHTmEUVz…Wk5E8Ssp
238d9885d6fddf…2397f49efb5774
13 in β†’ 1 out145.8323 XPM1.92 KB
AdnUrFmW…qqk34pco
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.

6.696 Γ— 10⁹³(94-digit number)
66961150934636834813…66877115753566840759
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
6.696 Γ— 10⁹³(94-digit number)
66961150934636834813…66877115753566840759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.696 Γ— 10⁹³(94-digit number)
66961150934636834813…66877115753566840761
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
1.339 Γ— 10⁹⁴(95-digit number)
13392230186927366962…33754231507133681519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.339 Γ— 10⁹⁴(95-digit number)
13392230186927366962…33754231507133681521
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
2.678 Γ— 10⁹⁴(95-digit number)
26784460373854733925…67508463014267363039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.678 Γ— 10⁹⁴(95-digit number)
26784460373854733925…67508463014267363041
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
5.356 Γ— 10⁹⁴(95-digit number)
53568920747709467850…35016926028534726079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.356 Γ— 10⁹⁴(95-digit number)
53568920747709467850…35016926028534726081
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
1.071 Γ— 10⁹⁡(96-digit number)
10713784149541893570…70033852057069452159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.071 Γ— 10⁹⁡(96-digit number)
10713784149541893570…70033852057069452161
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:57,723,347 XPMΒ·at block #6,809,907 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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