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Block #84,819

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2013, 1:42:36 AM Β· Difficulty 9.2787 Β· 6,709,887 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
18b2605031259863c4008990d03ba4f164055003940f393d3b3f8aaffef7df88
View on Chainz β†—

Height

#84,819

Difficulty

9.278745

Transactions

2

Size

723 B

Version

2

Bits

09475bda

Nonce

73,649

Timestamp

7/27/2013, 1:42:36 AM

Confirmations

6,709,887

Mined by

⛏️ P2SHAHSb9bTvKc5qGTJfbJ3qKpCEzHG4JUcbte

Merkle Root

c2123bed2d8e4a9f4dcb6411557a22567164bb13044afcfe36ec6cd46c952ead
Transactions (2)
Coinbase9eea3106a20dd8…d8fc64ee92a730
1 in β†’ 1 out11.6100 XPM109 B
AHSb9bTv…G4JUcbte
3163647d4e89b2…e1a5704c66f334
3 in β†’ 2 out55.3097 XPM522 B
AJTa341V…o9ioLKHuARxmAxSn…R3khZFpw
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.

3.466 Γ— 10⁹⁸(99-digit number)
34665202466720089386…23261451973990298499
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
3.466 Γ— 10⁹⁸(99-digit number)
34665202466720089386…23261451973990298499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.466 Γ— 10⁹⁸(99-digit number)
34665202466720089386…23261451973990298501
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
6.933 Γ— 10⁹⁸(99-digit number)
69330404933440178773…46522903947980596999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.933 Γ— 10⁹⁸(99-digit number)
69330404933440178773…46522903947980597001
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
1.386 Γ— 10⁹⁹(100-digit number)
13866080986688035754…93045807895961193999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.386 Γ— 10⁹⁹(100-digit number)
13866080986688035754…93045807895961194001
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
2.773 Γ— 10⁹⁹(100-digit number)
27732161973376071509…86091615791922387999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.773 Γ— 10⁹⁹(100-digit number)
27732161973376071509…86091615791922388001
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
5.546 Γ— 10⁹⁹(100-digit number)
55464323946752143018…72183231583844775999
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:57,601,695 XPMΒ·at block #6,794,705 Β· updates every 60s
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