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Block #2,816,376

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2018, 5:40:09 AM Β· Difficulty 11.6869 Β· 4,028,397 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
518415facaf75820a8a5e2724ee5fb252ddefbcfea1394b44a5fa2004369e865
View on Chainz β†—

Height

#2,816,376

Difficulty

11.686942

Transactions

2

Size

1018 B

Version

2

Bits

0bafdb6c

Nonce

2,007,715,658

Timestamp

8/30/2018, 5:40:09 AM

Confirmations

4,028,397

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

9fdbb14b4aaec98fde565f4ae3488db6e377499f36f37946d30ae4f4d3b8d70e
Transactions (2)
Coinbase3cd3bd52d9b7c3…390fce1af6e0a8
1 in β†’ 1 out7.3200 XPM109 B
AZtxQr2F…7grUWrUz
52c62a23de86c5…b58371ed2f7ae8
5 in β†’ 2 out4.0575 XPM819 B
AKGp1wvX…LZoDyAGxAQQqZZoo…bqo6MshV
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.

8.912 Γ— 10⁹⁡(96-digit number)
89124423315787426599…46330848069132181759
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
8.912 Γ— 10⁹⁡(96-digit number)
89124423315787426599…46330848069132181759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.912 Γ— 10⁹⁡(96-digit number)
89124423315787426599…46330848069132181761
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
1.782 Γ— 10⁹⁢(97-digit number)
17824884663157485319…92661696138264363519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.782 Γ— 10⁹⁢(97-digit number)
17824884663157485319…92661696138264363521
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
3.564 Γ— 10⁹⁢(97-digit number)
35649769326314970639…85323392276528727039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.564 Γ— 10⁹⁢(97-digit number)
35649769326314970639…85323392276528727041
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
7.129 Γ— 10⁹⁢(97-digit number)
71299538652629941279…70646784553057454079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.129 Γ— 10⁹⁢(97-digit number)
71299538652629941279…70646784553057454081
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
1.425 Γ— 10⁹⁷(98-digit number)
14259907730525988255…41293569106114908159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.425 Γ— 10⁹⁷(98-digit number)
14259907730525988255…41293569106114908161
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
2.851 Γ— 10⁹⁷(98-digit number)
28519815461051976511…82587138212229816319
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:58,002,597 XPMΒ·at block #6,844,772 Β· updates every 60s
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