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Block #2,995,903

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2019, 11:03:26 PM Β· Difficulty 11.2622

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7861e45b627ee81d32fac3f3687f434e24c2dd64b6f68a4e939f31526b7026bf
View on Chainz β†—

Height

#2,995,903

Difficulty

11.262174

Transactions

Timestamp

1/4/2019, 11:03:26 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.

6.210 Γ— 10⁹⁡(96-digit number)
62106933129698224731…80054518376092227839
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
6.210 Γ— 10⁹⁡(96-digit number)
62106933129698224731…80054518376092227839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.210 Γ— 10⁹⁡(96-digit number)
62106933129698224731…80054518376092227841
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
1.242 Γ— 10⁹⁢(97-digit number)
12421386625939644946…60109036752184455679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.242 Γ— 10⁹⁢(97-digit number)
12421386625939644946…60109036752184455681
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
2.484 Γ— 10⁹⁢(97-digit number)
24842773251879289892…20218073504368911359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.484 Γ— 10⁹⁢(97-digit number)
24842773251879289892…20218073504368911361
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
4.968 Γ— 10⁹⁢(97-digit number)
49685546503758579784…40436147008737822719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.968 Γ— 10⁹⁢(97-digit number)
49685546503758579784…40436147008737822721
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
9.937 Γ— 10⁹⁢(97-digit number)
99371093007517159569…80872294017475645439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.937 Γ— 10⁹⁢(97-digit number)
99371093007517159569…80872294017475645441
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
1.987 Γ— 10⁹⁷(98-digit number)
19874218601503431913…61744588034951290879
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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