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Block #2,272,046

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 3:36:34 PM Β· Difficulty 10.9541 Β· 4,564,523 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
707244dacc40af8183e25d75a01605d75c8dfa34be72b32103d8c1614181b6d0
View on Chainz β†—

Height

#2,272,046

Difficulty

10.954076

Transactions

2

Size

868 B

Version

2

Bits

0af43e59

Nonce

1,365,383,838

Timestamp

8/28/2017, 3:36:34 PM

Confirmations

4,564,523

Mined by

⛏️ P2SHAH6s5rPY9ct4WwgNptasfrzW7AoTuempqF

Merkle Root

1599fa449a33321abea9c4b6f63b76ff062f174c7d15c4d53ba0fdd0edf65715
Transactions (2)
Coinbase111527a458125c…8a2c13d482e416
1 in β†’ 1 out8.3300 XPM109 B
AH6s5rPY…oTuempqF
86ec7ecd01e1b3…9ae8dbe10830db
4 in β†’ 2 out1188.0166 XPM668 B
AS8Swa5k…emSJQqiEASCVMP9S…PtNfRh3C
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.

1.397 Γ— 10⁹⁷(98-digit number)
13970955675754289828…62239701452841943039
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
1.397 Γ— 10⁹⁷(98-digit number)
13970955675754289828…62239701452841943039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.397 Γ— 10⁹⁷(98-digit number)
13970955675754289828…62239701452841943041
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
2.794 Γ— 10⁹⁷(98-digit number)
27941911351508579657…24479402905683886079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.794 Γ— 10⁹⁷(98-digit number)
27941911351508579657…24479402905683886081
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
5.588 Γ— 10⁹⁷(98-digit number)
55883822703017159315…48958805811367772159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.588 Γ— 10⁹⁷(98-digit number)
55883822703017159315…48958805811367772161
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
1.117 Γ— 10⁹⁸(99-digit number)
11176764540603431863…97917611622735544319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.117 Γ— 10⁹⁸(99-digit number)
11176764540603431863…97917611622735544321
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
2.235 Γ— 10⁹⁸(99-digit number)
22353529081206863726…95835223245471088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.235 Γ— 10⁹⁸(99-digit number)
22353529081206863726…95835223245471088641
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
4.470 Γ— 10⁹⁸(99-digit number)
44707058162413727452…91670446490942177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.470 Γ— 10⁹⁸(99-digit number)
44707058162413727452…91670446490942177281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,936,817 XPMΒ·at block #6,836,568 Β· updates every 60s
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