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Block #2,757,613

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2018, 3:02:39 PM Β· Difficulty 11.6664 Β· 4,075,250 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c3eaf86945a371f1321095127ca410ddecea4e15082a4d9ceb5adfe7cb1451c
View on Chainz β†—

Height

#2,757,613

Difficulty

11.666384

Transactions

2

Size

720 B

Version

2

Bits

0baa982b

Nonce

326,296,503

Timestamp

7/20/2018, 3:02:39 PM

Confirmations

4,075,250

Mined by

⛏️ P2SHASJEse2Na4X6AgApTq745HBsaa2kHcFKti

Merkle Root

1d2f1f1f9df18e4afce809298e4c196ace0e4bfeaf9f3f029e59bed30a6ce9e7
Transactions (2)
Coinbase1dea7fa650db5a…2b3ca8cfc6555e
1 in β†’ 1 out7.3400 XPM110 B
ASJEse2N…2kHcFKti
6d3f8098f98d8b…33d7450a3d8115
3 in β†’ 2 out527.6678 XPM520 B
AbiZw7N1…HPacQJfkAVy5WKFV…2JatLg8j
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.

2.216 Γ— 10⁹⁡(96-digit number)
22166398275456358075…02947453251423544319
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
2.216 Γ— 10⁹⁡(96-digit number)
22166398275456358075…02947453251423544319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.216 Γ— 10⁹⁡(96-digit number)
22166398275456358075…02947453251423544321
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
4.433 Γ— 10⁹⁡(96-digit number)
44332796550912716151…05894906502847088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.433 Γ— 10⁹⁡(96-digit number)
44332796550912716151…05894906502847088641
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
8.866 Γ— 10⁹⁡(96-digit number)
88665593101825432303…11789813005694177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.866 Γ— 10⁹⁡(96-digit number)
88665593101825432303…11789813005694177281
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
1.773 Γ— 10⁹⁢(97-digit number)
17733118620365086460…23579626011388354559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.773 Γ— 10⁹⁢(97-digit number)
17733118620365086460…23579626011388354561
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
3.546 Γ— 10⁹⁢(97-digit number)
35466237240730172921…47159252022776709119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.546 Γ— 10⁹⁢(97-digit number)
35466237240730172921…47159252022776709121
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
7.093 Γ— 10⁹⁢(97-digit number)
70932474481460345842…94318504045553418239
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:57,907,073 XPMΒ·at block #6,832,862 Β· updates every 60s
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