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Block #2,812,023

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2018, 9:48:39 AM Β· Difficulty 11.6685 Β· 4,028,057 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4745aa8336e6fc5f3466e6ab9802bca13a1d79971c332ea389045e3704b7783
View on Chainz β†—

Height

#2,812,023

Difficulty

11.668544

Transactions

1

Size

200 B

Version

2

Bits

0bab25bb

Nonce

331,791,170

Timestamp

8/27/2018, 9:48:39 AM

Confirmations

4,028,057

Mined by

⛏️ P2SHAbKHJmwXbBErFpa7hfsrzPKvCeqzTVqpLe

Merkle Root

ddfed48c005055bee34202f2ff2e90113666c9c8a31bd87c919a178352e2f517
Transactions (1)
Coinbaseddfed48c005055…9a178352e2f517
1 in β†’ 1 out7.3300 XPM110 B
AbKHJmwX…qzTVqpLe
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.

6.240 Γ— 10⁹⁡(96-digit number)
62404015327808104959…92688642279242183679
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
6.240 Γ— 10⁹⁡(96-digit number)
62404015327808104959…92688642279242183679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.240 Γ— 10⁹⁡(96-digit number)
62404015327808104959…92688642279242183681
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
1.248 Γ— 10⁹⁢(97-digit number)
12480803065561620991…85377284558484367359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.248 Γ— 10⁹⁢(97-digit number)
12480803065561620991…85377284558484367361
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
2.496 Γ— 10⁹⁢(97-digit number)
24961606131123241983…70754569116968734719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.496 Γ— 10⁹⁢(97-digit number)
24961606131123241983…70754569116968734721
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
4.992 Γ— 10⁹⁢(97-digit number)
49923212262246483967…41509138233937469439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.992 Γ— 10⁹⁢(97-digit number)
49923212262246483967…41509138233937469441
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
9.984 Γ— 10⁹⁢(97-digit number)
99846424524492967935…83018276467874938879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.984 Γ— 10⁹⁢(97-digit number)
99846424524492967935…83018276467874938881
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
1.996 Γ— 10⁹⁷(98-digit number)
19969284904898593587…66036552935749877759
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:57,964,948 XPMΒ·at block #6,840,079 Β· updates every 60s
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