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Block #2,276,860

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2017, 10:15:05 PM Β· Difficulty 10.9551 Β· 4,556,070 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a2ce4365921ebdff1b93e807c3a531efc14cbd4288d6db25a8eeca58268eb50
View on Chainz β†—

Height

#2,276,860

Difficulty

10.955072

Transactions

1

Size

199 B

Version

2

Bits

0af47f9f

Nonce

955,461,851

Timestamp

8/31/2017, 10:15:05 PM

Confirmations

4,556,070

Mined by

⛏️ P2SHAaxoQkXCs1sDApCSzkWTW4mbJZ5mJmYjya

Merkle Root

4811e4fdfc8a2411975d3e5d988e65326c7e26cbef6ec5b8a501bcba040b8cfa
Transactions (1)
Coinbase4811e4fdfc8a24…01bcba040b8cfa
1 in β†’ 1 out8.3200 XPM109 B
AaxoQkXC…5mJmYjya
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.

5.516 Γ— 10⁹⁴(95-digit number)
55161442024537980338…75245692850162948759
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
5.516 Γ— 10⁹⁴(95-digit number)
55161442024537980338…75245692850162948759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.516 Γ— 10⁹⁴(95-digit number)
55161442024537980338…75245692850162948761
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
1.103 Γ— 10⁹⁡(96-digit number)
11032288404907596067…50491385700325897519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.103 Γ— 10⁹⁡(96-digit number)
11032288404907596067…50491385700325897521
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
2.206 Γ— 10⁹⁡(96-digit number)
22064576809815192135…00982771400651795039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.206 Γ— 10⁹⁡(96-digit number)
22064576809815192135…00982771400651795041
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
4.412 Γ— 10⁹⁡(96-digit number)
44129153619630384270…01965542801303590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.412 Γ— 10⁹⁡(96-digit number)
44129153619630384270…01965542801303590081
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
8.825 Γ— 10⁹⁡(96-digit number)
88258307239260768541…03931085602607180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.825 Γ— 10⁹⁡(96-digit number)
88258307239260768541…03931085602607180161
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
1.765 Γ— 10⁹⁢(97-digit number)
17651661447852153708…07862171205214360319
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:57,907,616 XPMΒ·at block #6,832,929 Β· updates every 60s
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