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Block #212,192

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 3:37:39 AM Β· Difficulty 9.9183 Β· 6,595,153 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bd02589ac5752736b5e89790e1feb18836a74aa161f44eb73e195eb3b98cce1b
View on Chainz β†—

Height

#212,192

Difficulty

9.918345

Transactions

1

Size

199 B

Version

2

Bits

09eb18a9

Nonce

16,789

Timestamp

10/16/2013, 3:37:39 AM

Confirmations

6,595,153

Mined by

⛏️ P2SHAPpAmzuiarcDRTEE9yddUu8j7EbKYJJ5pB

Merkle Root

083d9a49e835433f9252267d5f105f67abe9c84f5b6e2bdd4b145ec62afc5f79
Transactions (1)
Coinbase083d9a49e83543…145ec62afc5f79
1 in β†’ 1 out10.1500 XPM109 B
APpAmzui…bKYJJ5pB
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.

2.274 Γ— 10⁹⁡(96-digit number)
22740647944519777134…04824993542825084479
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
2.274 Γ— 10⁹⁡(96-digit number)
22740647944519777134…04824993542825084479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.274 Γ— 10⁹⁡(96-digit number)
22740647944519777134…04824993542825084481
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
4.548 Γ— 10⁹⁡(96-digit number)
45481295889039554268…09649987085650168959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.548 Γ— 10⁹⁡(96-digit number)
45481295889039554268…09649987085650168961
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
9.096 Γ— 10⁹⁡(96-digit number)
90962591778079108537…19299974171300337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.096 Γ— 10⁹⁡(96-digit number)
90962591778079108537…19299974171300337921
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
1.819 Γ— 10⁹⁢(97-digit number)
18192518355615821707…38599948342600675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.819 Γ— 10⁹⁢(97-digit number)
18192518355615821707…38599948342600675841
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
3.638 Γ— 10⁹⁢(97-digit number)
36385036711231643414…77199896685201351679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,702,780 XPMΒ·at block #6,807,344 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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