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Block #868,821

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/26/2014, 7:47:10 AM Β· Difficulty 10.9621 Β· 5,944,015 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
20ff0f716df941d5419f7f9e24e3f9e616fb83e99ee4203f8405c7f4c39187ab
View on Chainz β†—

Height

#868,821

Difficulty

10.962104

Transactions

2

Size

399 B

Version

2

Bits

0af64c7a

Nonce

946,706,637

Timestamp

12/26/2014, 7:47:10 AM

Confirmations

5,944,015

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9191ebf789232e26e4f4f47d30a3f361a0d5a28f5dc3abda1284787d3dc06f45
Transactions (2)
Coinbasee9f15f03376343…e3526ecb18b65c
1 in β†’ 1 out8.3202 XPM116 B
ANSXnLY2…Sd25TjkD
8f68bc06fec5ef…c1558965455850
1 in β†’ 1 out0.4900 XPM192 B
ANSQN9if…7RTf3UqW
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.

2.026 Γ— 10⁹⁢(97-digit number)
20266614869633273574…21373631117894304319
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
2.026 Γ— 10⁹⁢(97-digit number)
20266614869633273574…21373631117894304319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.026 Γ— 10⁹⁢(97-digit number)
20266614869633273574…21373631117894304321
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
4.053 Γ— 10⁹⁢(97-digit number)
40533229739266547149…42747262235788608639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.053 Γ— 10⁹⁢(97-digit number)
40533229739266547149…42747262235788608641
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
8.106 Γ— 10⁹⁢(97-digit number)
81066459478533094298…85494524471577217279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.106 Γ— 10⁹⁢(97-digit number)
81066459478533094298…85494524471577217281
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
1.621 Γ— 10⁹⁷(98-digit number)
16213291895706618859…70989048943154434559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16213291895706618859…70989048943154434561
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
3.242 Γ— 10⁹⁷(98-digit number)
32426583791413237719…41978097886308869119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.242 Γ— 10⁹⁷(98-digit number)
32426583791413237719…41978097886308869121
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
6.485 Γ— 10⁹⁷(98-digit number)
64853167582826475439…83956195772617738239
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:57,746,733 XPMΒ·at block #6,812,835 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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