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Block #1,886,195

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2016, 2:24:04 PM Β· Difficulty 10.7197 Β· 4,931,406 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eb7ddc7024a5d285b5fbe6f84c1273d190966477b12e7985ff6282baf4d32e18
View on Chainz β†—

Height

#1,886,195

Difficulty

10.719690

Transactions

2

Size

1.14 KB

Version

2

Bits

0ab83d93

Nonce

1,417,158,945

Timestamp

12/9/2016, 2:24:04 PM

Confirmations

4,931,406

Mined by

⛏️ P2SHALT95LNwJNtPzAU4YKRekLnQFgqs7zYDHT

Merkle Root

605149241083a5a413869151e72d10e1aadf4f09d88be6b3a811ff1f2bc6c0bd
Transactions (2)
Coinbasebc01a17f8ecddb…aa0170ad1e1e77
1 in β†’ 1 out8.7000 XPM109 B
ALT95LNw…qs7zYDHT
ca2f567253584e…b736bdcd11aa41
6 in β†’ 2 out35.9460 XPM967 B
ASMMZz4E…7FeHYYcpAGep1HUU…kuye4LRt
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.

3.703 Γ— 10⁹⁴(95-digit number)
37034156539496212127…81623569067564431359
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
3.703 Γ— 10⁹⁴(95-digit number)
37034156539496212127…81623569067564431359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.703 Γ— 10⁹⁴(95-digit number)
37034156539496212127…81623569067564431361
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
7.406 Γ— 10⁹⁴(95-digit number)
74068313078992424254…63247138135128862719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.406 Γ— 10⁹⁴(95-digit number)
74068313078992424254…63247138135128862721
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
1.481 Γ— 10⁹⁡(96-digit number)
14813662615798484850…26494276270257725439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.481 Γ— 10⁹⁡(96-digit number)
14813662615798484850…26494276270257725441
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
2.962 Γ— 10⁹⁡(96-digit number)
29627325231596969701…52988552540515450879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.962 Γ— 10⁹⁡(96-digit number)
29627325231596969701…52988552540515450881
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
5.925 Γ— 10⁹⁡(96-digit number)
59254650463193939403…05977105081030901759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.925 Γ— 10⁹⁡(96-digit number)
59254650463193939403…05977105081030901761
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:57,784,862 XPMΒ·at block #6,817,600 Β· updates every 60s
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