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Block #845,636

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2014, 12:43:57 AM Β· Difficulty 10.9725 Β· 5,985,688 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bc4707729d7110f8a787c68541fe179f9e6faafbad6bc1521611f04cc21f44b8
View on Chainz β†—

Height

#845,636

Difficulty

10.972458

Transactions

1

Size

206 B

Version

2

Bits

0af8f2fb

Nonce

2,228,277,837

Timestamp

12/9/2014, 12:43:57 AM

Confirmations

5,985,688

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ada61ae4c6146469fe1d741e38e68754a9ed474d801c4e4879246da769ad3065
Transactions (1)
Coinbaseada61ae4c61464…246da769ad3065
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.928 Γ— 10⁹⁡(96-digit number)
49280990533699661252…11827068335394528319
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
4.928 Γ— 10⁹⁡(96-digit number)
49280990533699661252…11827068335394528319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.928 Γ— 10⁹⁡(96-digit number)
49280990533699661252…11827068335394528321
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
9.856 Γ— 10⁹⁡(96-digit number)
98561981067399322504…23654136670789056639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.856 Γ— 10⁹⁡(96-digit number)
98561981067399322504…23654136670789056641
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
1.971 Γ— 10⁹⁢(97-digit number)
19712396213479864500…47308273341578113279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.971 Γ— 10⁹⁢(97-digit number)
19712396213479864500…47308273341578113281
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
3.942 Γ— 10⁹⁢(97-digit number)
39424792426959729001…94616546683156226559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.942 Γ— 10⁹⁢(97-digit number)
39424792426959729001…94616546683156226561
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
7.884 Γ— 10⁹⁢(97-digit number)
78849584853919458003…89233093366312453119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.884 Γ— 10⁹⁢(97-digit number)
78849584853919458003…89233093366312453121
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
1.576 Γ— 10⁹⁷(98-digit number)
15769916970783891600…78466186732624906239
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:57,894,744 XPMΒ·at block #6,831,323 Β· updates every 60s
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