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Block #2,170,021

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2017, 6:44:39 AM Β· Difficulty 10.9012 Β· 4,672,412 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56cd529e92e4a10f19d637124b43ce87e9919473bbb6b65f63b7d8c3a3e57b5a
View on Chainz β†—

Height

#2,170,021

Difficulty

10.901160

Transactions

2

Size

9.52 KB

Version

2

Bits

0ae6b26a

Nonce

1,289,453,395

Timestamp

6/21/2017, 6:44:39 AM

Confirmations

4,672,412

Mined by

⛏️ P2SHAUC9K97i4BAggGnRpcyQc68K7gg6X4Yhkh

Merkle Root

c1d11dee1c1d0dd12b1808ef23e10de28ec7279f62ca10c506836912d66c78a7
Transactions (2)
Coinbaseae7efb3bd7b91d…54e4b2bd0fc3c7
1 in β†’ 1 out8.5000 XPM109 B
AUC9K97i…g6X4Yhkh
8c9aa6eeaa8bda…e4269b5c14d991
64 in β†’ 2 out1317.5877 XPM9.32 KB
AVB8Kqgj…zUanL8TfARDyKKFT…SiJ6ZwNj
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.

3.679 Γ— 10⁹⁴(95-digit number)
36798785982838860770…74822664519614177279
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
3.679 Γ— 10⁹⁴(95-digit number)
36798785982838860770…74822664519614177279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.679 Γ— 10⁹⁴(95-digit number)
36798785982838860770…74822664519614177281
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
7.359 Γ— 10⁹⁴(95-digit number)
73597571965677721540…49645329039228354559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.359 Γ— 10⁹⁴(95-digit number)
73597571965677721540…49645329039228354561
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
1.471 Γ— 10⁹⁡(96-digit number)
14719514393135544308…99290658078456709119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.471 Γ— 10⁹⁡(96-digit number)
14719514393135544308…99290658078456709121
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
2.943 Γ— 10⁹⁡(96-digit number)
29439028786271088616…98581316156913418239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.943 Γ— 10⁹⁡(96-digit number)
29439028786271088616…98581316156913418241
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
5.887 Γ— 10⁹⁡(96-digit number)
58878057572542177232…97162632313826836479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.887 Γ— 10⁹⁡(96-digit number)
58878057572542177232…97162632313826836481
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:57,983,879 XPMΒ·at block #6,842,432 Β· updates every 60s
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