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Block #76,777

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/22/2013, 4:04:09 AM Β· Difficulty 9.1223 Β· 6,719,508 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82297b84aebe43dd9b066581c53e03bf71dd09c353751877021a95efa441a567
View on Chainz β†—

Height

#76,777

Difficulty

9.122302

Transactions

1

Size

199 B

Version

2

Bits

091f4f30

Nonce

395

Timestamp

7/22/2013, 4:04:09 AM

Confirmations

6,719,508

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

23ff6db87712b1657dfd3136434bb0675726d2245021b8f0fd698f7e6dcb451e
Transactions (1)
Coinbase23ff6db87712b1…698f7e6dcb451e
1 in β†’ 1 out12.0000 XPM110 B
AVQxbFsH…KG2vYXbz
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.

7.243 Γ— 10⁹²(93-digit number)
72435557827202416610…61888535892239802859
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
7.243 Γ— 10⁹²(93-digit number)
72435557827202416610…61888535892239802859
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.243 Γ— 10⁹²(93-digit number)
72435557827202416610…61888535892239802861
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
1.448 Γ— 10⁹³(94-digit number)
14487111565440483322…23777071784479605719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.448 Γ— 10⁹³(94-digit number)
14487111565440483322…23777071784479605721
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
2.897 Γ— 10⁹³(94-digit number)
28974223130880966644…47554143568959211439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.897 Γ— 10⁹³(94-digit number)
28974223130880966644…47554143568959211441
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
5.794 Γ— 10⁹³(94-digit number)
57948446261761933288…95108287137918422879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.794 Γ— 10⁹³(94-digit number)
57948446261761933288…95108287137918422881
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
1.158 Γ— 10⁹⁴(95-digit number)
11589689252352386657…90216574275836845759
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:57,614,283 XPMΒ·at block #6,796,284 Β· updates every 60s
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