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Block #2,844,373

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2018, 4:27:59 AM Β· Difficulty 11.7288 Β· 3,996,654 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bc5224768d388b525be68edec27681676e75299a9baae0af601d23a6c44a2ec2
View on Chainz β†—

Height

#2,844,373

Difficulty

11.728826

Transactions

2

Size

74.71 KB

Version

2

Bits

0bba945e

Nonce

357,219,520

Timestamp

9/18/2018, 4:27:59 AM

Confirmations

3,996,654

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

0745d0cb501e771b4828144286691080321ceedf632453217674e85b193c64fd
Transactions (2)
Coinbasecfa822734e2f0b…7dfbaa47d2e39f
1 in β†’ 1 out8.0900 XPM110 B
AZtxQr2F…7grUWrUz
5d999392248ee1…2ddf504be76111
515 in β†’ 2 out8000.0106 XPM74.51 KB
ALPF8J52…Hjw4BMsGAMoQ3AkJ…bU2wCT2w
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.

1.636 Γ— 10⁹⁢(97-digit number)
16363170488085985215…60127873378094387199
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
1.636 Γ— 10⁹⁢(97-digit number)
16363170488085985215…60127873378094387199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.636 Γ— 10⁹⁢(97-digit number)
16363170488085985215…60127873378094387201
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
3.272 Γ— 10⁹⁢(97-digit number)
32726340976171970430…20255746756188774399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.272 Γ— 10⁹⁢(97-digit number)
32726340976171970430…20255746756188774401
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
6.545 Γ— 10⁹⁢(97-digit number)
65452681952343940860…40511493512377548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.545 Γ— 10⁹⁢(97-digit number)
65452681952343940860…40511493512377548801
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
1.309 Γ— 10⁹⁷(98-digit number)
13090536390468788172…81022987024755097599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.309 Γ— 10⁹⁷(98-digit number)
13090536390468788172…81022987024755097601
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
2.618 Γ— 10⁹⁷(98-digit number)
26181072780937576344…62045974049510195199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.618 Γ— 10⁹⁷(98-digit number)
26181072780937576344…62045974049510195201
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
5.236 Γ— 10⁹⁷(98-digit number)
52362145561875152688…24091948099020390399
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:57,972,574 XPMΒ·at block #6,841,026 Β· updates every 60s
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