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Block #2,770,364

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2018, 1:40:22 PM Β· Difficulty 11.6583 Β· 4,071,716 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ecdbd181b9284967df1ab38b94835c75d6e7e3e9037ac163a9e14c61b480a4d
View on Chainz β†—

Height

#2,770,364

Difficulty

11.658304

Transactions

1

Size

199 B

Version

2

Bits

0ba88695

Nonce

1,912,138,506

Timestamp

7/29/2018, 1:40:22 PM

Confirmations

4,071,716

Mined by

⛏️ P2SHAKfoRRU2JCdWJ8SRBpXFUXkghrfXiQqPPK

Merkle Root

039df12b388e6497e6cdd43809ab93856d56f5ddc8352a5c384df48f47da6963
Transactions (1)
Coinbase039df12b388e64…4df48f47da6963
1 in β†’ 1 out7.3500 XPM110 B
AKfoRRU2…fXiQqPPK
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.

7.683 Γ— 10⁹¹(92-digit number)
76831123191444669678…70851175179721890479
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
7.683 Γ— 10⁹¹(92-digit number)
76831123191444669678…70851175179721890479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.683 Γ— 10⁹¹(92-digit number)
76831123191444669678…70851175179721890481
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
1.536 Γ— 10⁹²(93-digit number)
15366224638288933935…41702350359443780959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.536 Γ— 10⁹²(93-digit number)
15366224638288933935…41702350359443780961
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
3.073 Γ— 10⁹²(93-digit number)
30732449276577867871…83404700718887561919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.073 Γ— 10⁹²(93-digit number)
30732449276577867871…83404700718887561921
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
6.146 Γ— 10⁹²(93-digit number)
61464898553155735742…66809401437775123839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.146 Γ— 10⁹²(93-digit number)
61464898553155735742…66809401437775123841
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
1.229 Γ— 10⁹³(94-digit number)
12292979710631147148…33618802875550247679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.229 Γ— 10⁹³(94-digit number)
12292979710631147148…33618802875550247681
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
2.458 Γ— 10⁹³(94-digit number)
24585959421262294296…67237605751100495359
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:57,981,024 XPMΒ·at block #6,842,079 Β· updates every 60s
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