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Block #2,658,270

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/12/2018, 5:09:10 PM Β· Difficulty 11.6556 Β· 4,182,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
97539e7f53b2b68593a6b541cfec7817280f2c41dfb3a0b5669d28315c2800f8
View on Chainz β†—

Height

#2,658,270

Difficulty

11.655608

Transactions

2

Size

6.92 KB

Version

2

Bits

0ba7d5e9

Nonce

894,796,504

Timestamp

5/12/2018, 5:09:10 PM

Confirmations

4,182,192

Mined by

⛏️ P2SHAdnPdkQbwZcTzFjx6JpVfk9zyPvaSLRpJR

Merkle Root

b66e5f21f865a76f1392b31f8c365179d4d26b64a1f0b3509184df6c4895758f
Transactions (2)
Coinbasec06755660478a1…27043b6ee6f2e7
1 in β†’ 1 out7.4200 XPM109 B
AdnPdkQb…vaSLRpJR
405df16f8b6b9e…7fb8bdb70e3b03
46 in β†’ 2 out159.9895 XPM6.73 KB
AY2HjJuH…YW4vCSuTAJ8aGg4p…D4Zg3apq
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.

6.852 Γ— 10⁹⁴(95-digit number)
68524730026428460761…91945520307921805519
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
6.852 Γ— 10⁹⁴(95-digit number)
68524730026428460761…91945520307921805519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.852 Γ— 10⁹⁴(95-digit number)
68524730026428460761…91945520307921805521
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
1.370 Γ— 10⁹⁡(96-digit number)
13704946005285692152…83891040615843611039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.370 Γ— 10⁹⁡(96-digit number)
13704946005285692152…83891040615843611041
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
2.740 Γ— 10⁹⁡(96-digit number)
27409892010571384304…67782081231687222079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.740 Γ— 10⁹⁡(96-digit number)
27409892010571384304…67782081231687222081
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
5.481 Γ— 10⁹⁡(96-digit number)
54819784021142768609…35564162463374444159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.481 Γ— 10⁹⁡(96-digit number)
54819784021142768609…35564162463374444161
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
1.096 Γ— 10⁹⁢(97-digit number)
10963956804228553721…71128324926748888319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.096 Γ— 10⁹⁢(97-digit number)
10963956804228553721…71128324926748888321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.192 Γ— 10⁹⁢(97-digit number)
21927913608457107443…42256649853497776639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,968,024 XPMΒ·at block #6,840,461 Β· updates every 60s
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