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Block #96,099

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2013, 12:47:41 AM Β· Difficulty 9.2553 Β· 6,714,574 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b342d563f6e8b5f00e30c45fa85730454fc2003f54eabb9b43ed44b0508c8ea
View on Chainz β†—

Height

#96,099

Difficulty

9.255261

Transactions

2

Size

1.94 KB

Version

2

Bits

094158cd

Nonce

377

Timestamp

8/4/2013, 12:47:41 AM

Confirmations

6,714,574

Mined by

⛏️ P2SHASDVjbd8CHR1qesUPZSY88TTXrE8gHVANe

Merkle Root

39e22577938c6189fb80bc9dea6527b4f0de13f9c5af46997ae8b11fb4d7f21c
Transactions (2)
Coinbase72fec32ca02ff4…24258f5cde29c7
1 in β†’ 1 out11.6800 XPM110 B
ASDVjbd8…E8gHVANe
bedf484f8c9560…dade831072dd80
15 in β†’ 1 out165.5800 XPM1.75 KB
AMojYk3E…DzzgBLgu
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.

1.119 Γ— 10⁹³(94-digit number)
11192009842505293640…00889021421522486119
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
1.119 Γ— 10⁹³(94-digit number)
11192009842505293640…00889021421522486119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.119 Γ— 10⁹³(94-digit number)
11192009842505293640…00889021421522486121
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
2.238 Γ— 10⁹³(94-digit number)
22384019685010587281…01778042843044972239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.238 Γ— 10⁹³(94-digit number)
22384019685010587281…01778042843044972241
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
4.476 Γ— 10⁹³(94-digit number)
44768039370021174562…03556085686089944479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.476 Γ— 10⁹³(94-digit number)
44768039370021174562…03556085686089944481
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
8.953 Γ— 10⁹³(94-digit number)
89536078740042349124…07112171372179888959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.953 Γ— 10⁹³(94-digit number)
89536078740042349124…07112171372179888961
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
1.790 Γ— 10⁹⁴(95-digit number)
17907215748008469824…14224342744359777919
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:57,729,475 XPMΒ·at block #6,810,672 Β· updates every 60s
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