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Block #2,762,910

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2018, 10:06:27 AM Β· Difficulty 11.6553 Β· 4,075,844 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0338302df56e4f92d5ccd0093bd5cfb3410ba5d57000f3e7eb7794d4b370bcb5
View on Chainz β†—

Height

#2,762,910

Difficulty

11.655328

Transactions

1

Size

200 B

Version

2

Bits

0ba7c38d

Nonce

416,059,160

Timestamp

7/24/2018, 10:06:27 AM

Confirmations

4,075,844

Mined by

⛏️ P2SHAHBXiVcJGpAMBh8n42DNdi1gXUof3bNpVB

Merkle Root

6c86f88f4371b2e3bce2764a8002b49ce9bfefc4e130caaa67f368d9c0f21c43
Transactions (1)
Coinbase6c86f88f4371b2…f368d9c0f21c43
1 in β†’ 1 out7.3500 XPM110 B
AHBXiVcJ…of3bNpVB
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.

2.433 Γ— 10⁹⁡(96-digit number)
24339381057660104018…71428119932244515839
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
2.433 Γ— 10⁹⁡(96-digit number)
24339381057660104018…71428119932244515839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.433 Γ— 10⁹⁡(96-digit number)
24339381057660104018…71428119932244515841
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
4.867 Γ— 10⁹⁡(96-digit number)
48678762115320208037…42856239864489031679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.867 Γ— 10⁹⁡(96-digit number)
48678762115320208037…42856239864489031681
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
9.735 Γ— 10⁹⁡(96-digit number)
97357524230640416075…85712479728978063359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.735 Γ— 10⁹⁡(96-digit number)
97357524230640416075…85712479728978063361
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
1.947 Γ— 10⁹⁢(97-digit number)
19471504846128083215…71424959457956126719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.947 Γ— 10⁹⁢(97-digit number)
19471504846128083215…71424959457956126721
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
3.894 Γ— 10⁹⁢(97-digit number)
38943009692256166430…42849918915912253439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.894 Γ— 10⁹⁢(97-digit number)
38943009692256166430…42849918915912253441
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
7.788 Γ— 10⁹⁢(97-digit number)
77886019384512332860…85699837831824506879
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
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