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Block #82,072

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2013, 4:28:34 AM Β· Difficulty 9.2735 Β· 6,728,747 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5af4ed08dc8806cb2052b316ad90f55bda0dfc4b0ccfc5de2a544a543de2f492
View on Chainz β†—

Height

#82,072

Difficulty

9.273497

Transactions

1

Size

200 B

Version

2

Bits

094603ee

Nonce

235,930

Timestamp

7/25/2013, 4:28:34 AM

Confirmations

6,728,747

Mined by

⛏️ P2SHAbmC177FbWsA3xjDrM8MdR2hvjpomdGgdX

Merkle Root

5cb35d8891257fe0ff247f48b28e49e43337e684d56f883ba38119ebea414567
Transactions (1)
Coinbase5cb35d8891257f…8119ebea414567
1 in β†’ 1 out11.6100 XPM109 B
AbmC177F…pomdGgdX
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.

1.193 Γ— 10⁹⁸(99-digit number)
11934411803060730562…83613670245164767399
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
1.193 Γ— 10⁹⁸(99-digit number)
11934411803060730562…83613670245164767399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.193 Γ— 10⁹⁸(99-digit number)
11934411803060730562…83613670245164767401
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
2.386 Γ— 10⁹⁸(99-digit number)
23868823606121461125…67227340490329534799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.386 Γ— 10⁹⁸(99-digit number)
23868823606121461125…67227340490329534801
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
4.773 Γ— 10⁹⁸(99-digit number)
47737647212242922251…34454680980659069599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.773 Γ— 10⁹⁸(99-digit number)
47737647212242922251…34454680980659069601
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
9.547 Γ— 10⁹⁸(99-digit number)
95475294424485844502…68909361961318139199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.547 Γ— 10⁹⁸(99-digit number)
95475294424485844502…68909361961318139201
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
1.909 Γ— 10⁹⁹(100-digit number)
19095058884897168900…37818723922636278399
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:57,730,654 XPMΒ·at block #6,810,818 Β· updates every 60s
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