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Block #2,742,974

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/10/2018, 7:08:53 PM Β· Difficulty 11.6322

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f60910a10bf256c78c9c4a4ce37211dafc0ae9753954b34cfe685d0ccb34dfbc
View on Chainz β†—

Height

#2,742,974

Difficulty

11.632166

Transactions

Timestamp

7/10/2018, 7:08:53 PM

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.

1.211 Γ— 10⁹⁢(97-digit number)
12118219882827735822…74330943511986175999
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
1.211 Γ— 10⁹⁢(97-digit number)
12118219882827735822…74330943511986175999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.211 Γ— 10⁹⁢(97-digit number)
12118219882827735822…74330943511986176001
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
2.423 Γ— 10⁹⁢(97-digit number)
24236439765655471644…48661887023972351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.423 Γ— 10⁹⁢(97-digit number)
24236439765655471644…48661887023972352001
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
4.847 Γ— 10⁹⁢(97-digit number)
48472879531310943288…97323774047944703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.847 Γ— 10⁹⁢(97-digit number)
48472879531310943288…97323774047944704001
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
9.694 Γ— 10⁹⁢(97-digit number)
96945759062621886577…94647548095889407999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.694 Γ— 10⁹⁢(97-digit number)
96945759062621886577…94647548095889408001
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
1.938 Γ— 10⁹⁷(98-digit number)
19389151812524377315…89295096191778815999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.938 Γ— 10⁹⁷(98-digit number)
19389151812524377315…89295096191778816001
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
3.877 Γ— 10⁹⁷(98-digit number)
38778303625048754630…78590192383557631999
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:β€”
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