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Block #95,365

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/3/2013, 4:10:45 PM Β· Difficulty 9.2201 Β· 6,708,521 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
07bad727c971e57e73937876ba83cf15a54f9ae78ea3cb84051a94e47542f45a
View on Chainz β†—

Height

#95,365

Difficulty

9.220074

Transactions

2

Size

1.14 KB

Version

2

Bits

093856cc

Nonce

472,767

Timestamp

8/3/2013, 4:10:45 PM

Confirmations

6,708,521

Mined by

⛏️ P2SHAVez4SqqHwoDYj8NoeSk1S7ZLCYVd2CyRi

Merkle Root

84aa260ffd8bc6feea34e73d11427941d5270e01c9f0a8073c36b5bebcd42ffc
Transactions (2)
Coinbase7188ad4c245ccf…a98f57e7caa49a
1 in β†’ 1 out11.7600 XPM109 B
AVez4Sqq…YVd2CyRi
d807161b768f61…32814a72378ef8
6 in β†’ 2 out51.1542 XPM963 B
AJsCpFR2…BoQVqzZxAJDoe6Jv…1Tn3YYeh
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.

7.188 Γ— 10⁹⁷(98-digit number)
71881017785235899061…09214746472854883339
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
7.188 Γ— 10⁹⁷(98-digit number)
71881017785235899061…09214746472854883339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.188 Γ— 10⁹⁷(98-digit number)
71881017785235899061…09214746472854883341
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
1.437 Γ— 10⁹⁸(99-digit number)
14376203557047179812…18429492945709766679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.437 Γ— 10⁹⁸(99-digit number)
14376203557047179812…18429492945709766681
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
2.875 Γ— 10⁹⁸(99-digit number)
28752407114094359624…36858985891419533359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.875 Γ— 10⁹⁸(99-digit number)
28752407114094359624…36858985891419533361
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
5.750 Γ— 10⁹⁸(99-digit number)
57504814228188719249…73717971782839066719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.750 Γ— 10⁹⁸(99-digit number)
57504814228188719249…73717971782839066721
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
1.150 Γ— 10⁹⁹(100-digit number)
11500962845637743849…47435943565678133439
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:57,675,131 XPMΒ·at block #6,803,885 Β· updates every 60s
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