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Block #2,736,030

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/6/2018, 4:28:55 AM Β· Difficulty 11.6091 Β· 4,101,463 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0cc4c89beb4b86f75c1fe175d03527168af322592c26171b9dea4f4ce291503b
View on Chainz β†—

Height

#2,736,030

Difficulty

11.609125

Transactions

2

Size

10.69 KB

Version

2

Bits

0b9befa1

Nonce

365,435,232

Timestamp

7/6/2018, 4:28:55 AM

Confirmations

4,101,463

Mined by

⛏️ P2SHAQdJ5MQygasu52WBndX26FkgzgahDgsvf6

Merkle Root

5149172ab2b5c7bd85a824300b2b7575edd8758d92ea646468c3680c74f3ee36
Transactions (2)
Coinbaseb33fbd1e6d0d22…d2d47b9faa8809
1 in β†’ 1 out7.5400 XPM109 B
AQdJ5MQy…ahDgsvf6
c77e604cb2d946…6a5dfe3fb98a0f
72 in β†’ 2 out647.7452 XPM10.49 KB
ANSt9ABz…2J5riagjAXgn8nEk…rzi3LXnq
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.

2.107 Γ— 10⁹⁢(97-digit number)
21073037418322229014…32870383258811217919
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
2.107 Γ— 10⁹⁢(97-digit number)
21073037418322229014…32870383258811217919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.107 Γ— 10⁹⁢(97-digit number)
21073037418322229014…32870383258811217921
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
4.214 Γ— 10⁹⁢(97-digit number)
42146074836644458029…65740766517622435839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.214 Γ— 10⁹⁢(97-digit number)
42146074836644458029…65740766517622435841
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
8.429 Γ— 10⁹⁢(97-digit number)
84292149673288916058…31481533035244871679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.429 Γ— 10⁹⁢(97-digit number)
84292149673288916058…31481533035244871681
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
1.685 Γ— 10⁹⁷(98-digit number)
16858429934657783211…62963066070489743359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.685 Γ— 10⁹⁷(98-digit number)
16858429934657783211…62963066070489743361
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
3.371 Γ— 10⁹⁷(98-digit number)
33716859869315566423…25926132140979486719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.371 Γ— 10⁹⁷(98-digit number)
33716859869315566423…25926132140979486721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.743 Γ— 10⁹⁷(98-digit number)
67433719738631132847…51852264281958973439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,944,265 XPMΒ·at block #6,837,492 Β· updates every 60s
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