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Block #192,091

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/3/2013, 3:12:47 PM Β· Difficulty 9.8747 Β· 6,634,991 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
601a3c61d60443167f7b9d1a58b8352ae9f431863f1f75a5dd06e5ce1ae685e3
View on Chainz β†—

Height

#192,091

Difficulty

9.874717

Transactions

1

Size

199 B

Version

2

Bits

09dfed73

Nonce

306,445

Timestamp

10/3/2013, 3:12:47 PM

Confirmations

6,634,991

Mined by

⛏️ P2SHAXX6Uqo66gbvicjAJn7bP5KsLHr1CYovnd

Merkle Root

b97fb54f5c35c1bc200c7c5da9d10296afc8172106cc00ba6b03bc066dae6660
Transactions (1)
Coinbaseb97fb54f5c35c1…03bc066dae6660
1 in β†’ 1 out10.2400 XPM109 B
AXX6Uqo6…r1CYovnd
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.

6.011 Γ— 10⁹⁴(95-digit number)
60111557330960171743…23207045571662506879
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
6.011 Γ— 10⁹⁴(95-digit number)
60111557330960171743…23207045571662506879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.011 Γ— 10⁹⁴(95-digit number)
60111557330960171743…23207045571662506881
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
1.202 Γ— 10⁹⁡(96-digit number)
12022311466192034348…46414091143325013759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.202 Γ— 10⁹⁡(96-digit number)
12022311466192034348…46414091143325013761
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
2.404 Γ— 10⁹⁡(96-digit number)
24044622932384068697…92828182286650027519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.404 Γ— 10⁹⁡(96-digit number)
24044622932384068697…92828182286650027521
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
4.808 Γ— 10⁹⁡(96-digit number)
48089245864768137395…85656364573300055039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.808 Γ— 10⁹⁡(96-digit number)
48089245864768137395…85656364573300055041
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
9.617 Γ— 10⁹⁡(96-digit number)
96178491729536274790…71312729146600110079
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:57,860,841 XPMΒ·at block #6,827,081 Β· updates every 60s
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