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Block #2,279,141

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2017, 10:53:00 AM Β· Difficulty 10.9559 Β· 4,563,800 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cdea34e23b8c470040849f98db24dfb2afbcf7a64c155b6d98a61cafd499feb3
View on Chainz β†—

Height

#2,279,141

Difficulty

10.955872

Transactions

1

Size

200 B

Version

2

Bits

0af4b40d

Nonce

1,135,809,277

Timestamp

9/2/2017, 10:53:00 AM

Confirmations

4,563,800

Mined by

⛏️ P2SHAaenCPrn9kmaj9oiudARa7MMuJCu6QH1H5

Merkle Root

390b13c3827328f543f985655259cf02b96434b02503eac9c632d725e2fa89c8
Transactions (1)
Coinbase390b13c3827328…32d725e2fa89c8
1 in β†’ 1 out8.3200 XPM110 B
AaenCPrn…Cu6QH1H5
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.

2.636 Γ— 10⁹⁴(95-digit number)
26366658735462138356…07370667444651318159
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
2.636 Γ— 10⁹⁴(95-digit number)
26366658735462138356…07370667444651318159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.636 Γ— 10⁹⁴(95-digit number)
26366658735462138356…07370667444651318161
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
5.273 Γ— 10⁹⁴(95-digit number)
52733317470924276712…14741334889302636319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.273 Γ— 10⁹⁴(95-digit number)
52733317470924276712…14741334889302636321
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
1.054 Γ— 10⁹⁡(96-digit number)
10546663494184855342…29482669778605272639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.054 Γ— 10⁹⁡(96-digit number)
10546663494184855342…29482669778605272641
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
2.109 Γ— 10⁹⁡(96-digit number)
21093326988369710685…58965339557210545279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.109 Γ— 10⁹⁡(96-digit number)
21093326988369710685…58965339557210545281
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
4.218 Γ— 10⁹⁡(96-digit number)
42186653976739421370…17930679114421090559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.218 Γ— 10⁹⁡(96-digit number)
42186653976739421370…17930679114421090561
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
8.437 Γ— 10⁹⁡(96-digit number)
84373307953478842740…35861358228842181119
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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