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Block #798,304

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/5/2014, 9:52:04 AM Β· Difficulty 10.9764 Β· 6,018,576 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
44a34fe84aeff0ff0cfb5b3b609e64840578cfd6787299dc8370f2152e4eb29f
View on Chainz β†—

Height

#798,304

Difficulty

10.976377

Transactions

1

Size

242 B

Version

2

Bits

0af9f3db

Nonce

272,662,918

Timestamp

11/5/2014, 9:52:04 AM

Confirmations

6,018,576

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

fb8045cc03180992d764247789c1aad662302387650608cc19ff0700d2342eeb
Transactions (1)
Coinbasefb8045cc031809…ff0700d2342eeb
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…EJXLjVFh
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.

5.272 Γ— 10⁹⁴(95-digit number)
52728149233750655446…53916615099843992849
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
5.272 Γ— 10⁹⁴(95-digit number)
52728149233750655446…53916615099843992849
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.272 Γ— 10⁹⁴(95-digit number)
52728149233750655446…53916615099843992851
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
1.054 Γ— 10⁹⁡(96-digit number)
10545629846750131089…07833230199687985699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.054 Γ— 10⁹⁡(96-digit number)
10545629846750131089…07833230199687985701
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
2.109 Γ— 10⁹⁡(96-digit number)
21091259693500262178…15666460399375971399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.109 Γ— 10⁹⁡(96-digit number)
21091259693500262178…15666460399375971401
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
4.218 Γ— 10⁹⁡(96-digit number)
42182519387000524357…31332920798751942799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.218 Γ— 10⁹⁡(96-digit number)
42182519387000524357…31332920798751942801
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
8.436 Γ— 10⁹⁡(96-digit number)
84365038774001048714…62665841597503885599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.436 Γ— 10⁹⁡(96-digit number)
84365038774001048714…62665841597503885601
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
1.687 Γ— 10⁹⁢(97-digit number)
16873007754800209742…25331683195007771199
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:57,779,079 XPMΒ·at block #6,816,879 Β· updates every 60s
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