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Block #191,095

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2013, 9:52:56 PM Β· Difficulty 9.8757 Β· 6,636,060 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cc72feb9c73d5bbe199a458c1c329ef1cf057c6e46e1398e6dc176ae0786e705
View on Chainz β†—

Height

#191,095

Difficulty

9.875676

Transactions

1

Size

199 B

Version

2

Bits

09e02c4f

Nonce

285,809

Timestamp

10/2/2013, 9:52:56 PM

Confirmations

6,636,060

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

92fdaad12738bbcfd42d321370a88e235bda3e816b3557ce6cf1ba78c1c4fd96
Transactions (1)
Coinbase92fdaad12738bb…f1ba78c1c4fd96
1 in β†’ 1 out10.2400 XPM109 B
AbJUC2oS…cpKam6LK
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.

1.609 Γ— 10⁹⁡(96-digit number)
16097242380483047011…12480376415583148799
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
1.609 Γ— 10⁹⁡(96-digit number)
16097242380483047011…12480376415583148799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.609 Γ— 10⁹⁡(96-digit number)
16097242380483047011…12480376415583148801
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
3.219 Γ— 10⁹⁡(96-digit number)
32194484760966094022…24960752831166297599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.219 Γ— 10⁹⁡(96-digit number)
32194484760966094022…24960752831166297601
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
6.438 Γ— 10⁹⁡(96-digit number)
64388969521932188044…49921505662332595199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.438 Γ— 10⁹⁡(96-digit number)
64388969521932188044…49921505662332595201
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
1.287 Γ— 10⁹⁢(97-digit number)
12877793904386437608…99843011324665190399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.287 Γ— 10⁹⁢(97-digit number)
12877793904386437608…99843011324665190401
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
2.575 Γ— 10⁹⁢(97-digit number)
25755587808772875217…99686022649330380799
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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