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Block #2,811,918

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2018, 8:03:47 AM Β· Difficulty 11.6685 Β· 4,019,265 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eb9e646a456d4bc6291d706d0142b20357e6791b6a3aca4107905422ed6947ea
View on Chainz β†—

Height

#2,811,918

Difficulty

11.668507

Transactions

2

Size

1.14 KB

Version

2

Bits

0bab2344

Nonce

1,814,578,685

Timestamp

8/27/2018, 8:03:47 AM

Confirmations

4,019,265

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

8dc00204379f4886384427ba190cbdc8965974210475a5d16cd2fdf3e8ffe5c1
Transactions (2)
Coinbasef754e8934202ae…ed01d46295b181
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
656322e3b7ae98…3d70459adf1bfd
6 in β†’ 2 out311.1723 XPM963 B
APkK7USv…wsxQDuTHAJdM6BQD…g1g59wty
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.

8.698 Γ— 10⁹⁡(96-digit number)
86984912743210992726…76405525671504312319
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
8.698 Γ— 10⁹⁡(96-digit number)
86984912743210992726…76405525671504312319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.698 Γ— 10⁹⁡(96-digit number)
86984912743210992726…76405525671504312321
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
1.739 Γ— 10⁹⁢(97-digit number)
17396982548642198545…52811051343008624639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.739 Γ— 10⁹⁢(97-digit number)
17396982548642198545…52811051343008624641
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
3.479 Γ— 10⁹⁢(97-digit number)
34793965097284397090…05622102686017249279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.479 Γ— 10⁹⁢(97-digit number)
34793965097284397090…05622102686017249281
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
6.958 Γ— 10⁹⁢(97-digit number)
69587930194568794181…11244205372034498559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.958 Γ— 10⁹⁢(97-digit number)
69587930194568794181…11244205372034498561
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
1.391 Γ— 10⁹⁷(98-digit number)
13917586038913758836…22488410744068997119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.391 Γ— 10⁹⁷(98-digit number)
13917586038913758836…22488410744068997121
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
2.783 Γ— 10⁹⁷(98-digit number)
27835172077827517672…44976821488137994239
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:57,893,607 XPMΒ·at block #6,831,182 Β· updates every 60s
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