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Block #2,095,746

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2017, 12:54:34 PM Β· Difficulty 10.8716 Β· 4,748,761 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
81375c97444f831a9dd09d85c3a3051c91408695decda4bbaa67e4e9c164e04e
View on Chainz β†—

Height

#2,095,746

Difficulty

10.871574

Transactions

2

Size

2.00 KB

Version

2

Bits

0adf1f79

Nonce

205,627,105

Timestamp

5/1/2017, 12:54:34 PM

Confirmations

4,748,761

Mined by

⛏️ P2SHAMomRrgShiw3fA4Xd1oW3vzyx6xUgLWDA2

Merkle Root

65cb5fce6e392b2b723889079cc3a75b125989c50ca9640ba1c0ef82ec716152
Transactions (2)
Coinbase30c40a8753abc8…51dd371cf1f4d9
1 in β†’ 1 out8.4700 XPM109 B
AMomRrgS…xUgLWDA2
1734805b086d42…2b6b1fcf546ef8
12 in β†’ 2 out884.1756 XPM1.81 KB
AUTDBM55…mz4rGxPPAYJMR38i…5MGvCdGN
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.

8.098 Γ— 10⁹³(94-digit number)
80983888707110638889…84878670704960099919
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
8.098 Γ— 10⁹³(94-digit number)
80983888707110638889…84878670704960099919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.098 Γ— 10⁹³(94-digit number)
80983888707110638889…84878670704960099921
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
1.619 Γ— 10⁹⁴(95-digit number)
16196777741422127777…69757341409920199839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.619 Γ— 10⁹⁴(95-digit number)
16196777741422127777…69757341409920199841
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
3.239 Γ— 10⁹⁴(95-digit number)
32393555482844255555…39514682819840399679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.239 Γ— 10⁹⁴(95-digit number)
32393555482844255555…39514682819840399681
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
6.478 Γ— 10⁹⁴(95-digit number)
64787110965688511111…79029365639680799359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.478 Γ— 10⁹⁴(95-digit number)
64787110965688511111…79029365639680799361
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
1.295 Γ— 10⁹⁡(96-digit number)
12957422193137702222…58058731279361598719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.295 Γ— 10⁹⁡(96-digit number)
12957422193137702222…58058731279361598721
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
2.591 Γ— 10⁹⁡(96-digit number)
25914844386275404444…16117462558723197439
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:58,000,454 XPMΒ·at block #6,844,506 Β· updates every 60s
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