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Block #804,649

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/10/2014, 12:25:56 AM Β· Difficulty 10.9752 Β· 5,994,706 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b749a5dd587254daa598eb00b7d70818976b197c0de4545c023a533fd0212707
View on Chainz β†—

Height

#804,649

Difficulty

10.975197

Transactions

3

Size

1.08 KB

Version

2

Bits

0af9a68b

Nonce

402,590,410

Timestamp

11/10/2014, 12:25:56 AM

Confirmations

5,994,706

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1d0eef301fbc2d340b6f2519bf6abb7e7fbfacc1c087b9813807d278cc099428
Transactions (3)
Coinbasebe870015b95af5…b417740d91053b
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
eeeebfe18f6152…33ba3e27e7b68e
4 in β†’ 2 out25.0185 XPM670 B
AbreMMbU…9yQCEF7BASZ34J1q…6tttt8Au
513f38eeaec935…8b85fe7a35b764
1 in β†’ 2 out0.8466 XPM226 B
AewzBMQ4…jh6Lr6ygAKUvR6c6…PjpFWiw2
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.

1.053 Γ— 10⁹⁹(100-digit number)
10532026764127957254…44792655967334563839
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
1.053 Γ— 10⁹⁹(100-digit number)
10532026764127957254…44792655967334563839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.053 Γ— 10⁹⁹(100-digit number)
10532026764127957254…44792655967334563841
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
2.106 Γ— 10⁹⁹(100-digit number)
21064053528255914509…89585311934669127679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.106 Γ— 10⁹⁹(100-digit number)
21064053528255914509…89585311934669127681
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
4.212 Γ— 10⁹⁹(100-digit number)
42128107056511829019…79170623869338255359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.212 Γ— 10⁹⁹(100-digit number)
42128107056511829019…79170623869338255361
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
8.425 Γ— 10⁹⁹(100-digit number)
84256214113023658038…58341247738676510719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.425 Γ— 10⁹⁹(100-digit number)
84256214113023658038…58341247738676510721
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
1.685 Γ— 10¹⁰⁰(101-digit number)
16851242822604731607…16682495477353021439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.685 Γ— 10¹⁰⁰(101-digit number)
16851242822604731607…16682495477353021441
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
3.370 Γ— 10¹⁰⁰(101-digit number)
33702485645209463215…33364990954706042879
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:57,638,885 XPMΒ·at block #6,799,354 Β· updates every 60s
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