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Block #162,185

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 3:43:14 AM Β· Difficulty 9.8609 Β· 6,634,395 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6f38839a735835a3257db49522517edc207160facf49e4a08a7daabb1abe8c63
View on Chainz β†—

Height

#162,185

Difficulty

9.860883

Transactions

2

Size

1.85 KB

Version

2

Bits

09dc62d5

Nonce

41,754

Timestamp

9/13/2013, 3:43:14 AM

Confirmations

6,634,395

Mined by

⛏️ P2SHANbgq2LN5bBnWnbN5T5qKjbtRD4qCSqfXi

Merkle Root

27c0fccd4ec0452a52c034232a5d9ac677ade772ba402881b70d9fe41904e816
Transactions (2)
Coinbasedc339e6d467258…de46864742dd6e
1 in β†’ 1 out10.2900 XPM109 B
ANbgq2LN…4qCSqfXi
cc7aba850165d8…952a2bc0c310df
13 in β†’ 2 out109.5043 XPM1.66 KB
AU6MHXiz…efY91cHZAcd1BgN5…bE5c9NoN
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.

9.522 Γ— 10⁸⁸(89-digit number)
95228981873601911857…56413710435807224779
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
9.522 Γ— 10⁸⁸(89-digit number)
95228981873601911857…56413710435807224779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.522 Γ— 10⁸⁸(89-digit number)
95228981873601911857…56413710435807224781
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
1.904 Γ— 10⁸⁹(90-digit number)
19045796374720382371…12827420871614449559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.904 Γ— 10⁸⁹(90-digit number)
19045796374720382371…12827420871614449561
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
3.809 Γ— 10⁸⁹(90-digit number)
38091592749440764742…25654841743228899119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.809 Γ— 10⁸⁹(90-digit number)
38091592749440764742…25654841743228899121
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
7.618 Γ— 10⁸⁹(90-digit number)
76183185498881529485…51309683486457798239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.618 Γ— 10⁸⁹(90-digit number)
76183185498881529485…51309683486457798241
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
1.523 Γ— 10⁹⁰(91-digit number)
15236637099776305897…02619366972915596479
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:57,616,642 XPMΒ·at block #6,796,579 Β· updates every 60s
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