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Block #212,169

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 3:16:15 AM Β· Difficulty 9.9183 Β· 6,594,964 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d23d8093fbb706747411c1f64eef0eeae6abdf9470fc3dcc310b22b8855fe90
View on Chainz β†—

Height

#212,169

Difficulty

9.918308

Transactions

1

Size

200 B

Version

2

Bits

09eb1641

Nonce

46,963

Timestamp

10/16/2013, 3:16:15 AM

Confirmations

6,594,964

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

5bbacfa4406b38fd13cd898399c07da394ef06b6abc94e81f2a44b7170fa0f71
Transactions (1)
Coinbase5bbacfa4406b38…a44b7170fa0f71
1 in β†’ 1 out10.1500 XPM110 B
AbuU1HhS…JPwsJEbB
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.

2.481 Γ— 10⁹⁡(96-digit number)
24812786944939932977…78375385091075295999
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
2.481 Γ— 10⁹⁡(96-digit number)
24812786944939932977…78375385091075295999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.481 Γ— 10⁹⁡(96-digit number)
24812786944939932977…78375385091075296001
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
4.962 Γ— 10⁹⁡(96-digit number)
49625573889879865954…56750770182150591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.962 Γ— 10⁹⁡(96-digit number)
49625573889879865954…56750770182150592001
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
9.925 Γ— 10⁹⁡(96-digit number)
99251147779759731909…13501540364301183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.925 Γ— 10⁹⁡(96-digit number)
99251147779759731909…13501540364301184001
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
1.985 Γ— 10⁹⁢(97-digit number)
19850229555951946381…27003080728602367999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.985 Γ— 10⁹⁢(97-digit number)
19850229555951946381…27003080728602368001
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
3.970 Γ— 10⁹⁢(97-digit number)
39700459111903892763…54006161457204735999
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:57,701,169 XPMΒ·at block #6,807,132 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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