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Block #242,240

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/3/2013, 3:43:20 PM Β· Difficulty 9.9594 Β· 6,574,196 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d775e24e1856a5b342670af084d87c16cd8936172694b813e148351a33d6ab2
View on Chainz β†—

Height

#242,240

Difficulty

9.959392

Transactions

2

Size

392 B

Version

2

Bits

09f59abc

Nonce

22,471

Timestamp

11/3/2013, 3:43:20 PM

Confirmations

6,574,196

Mined by

⛏️ P2SHAMVefmpoaYJpYap51AmLso4ahnPv5VsQCv

Merkle Root

98ae9e359771c498b203276b9dc825a203504ab2c750bed04d32600e8cf6024c
Transactions (2)
Coinbaseb4a15737b9c91b…a37117b153fe3a
1 in β†’ 1 out10.0800 XPM109 B
AMVefmpo…Pv5VsQCv
bb9789819fb617…109316b4be007b
1 in β†’ 1 out130.0045 XPM193 B
ATknEwpv…tz6xvy1e
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.

2.504 Γ— 10⁹⁴(95-digit number)
25040736964569129187…83631105273444270399
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
2.504 Γ— 10⁹⁴(95-digit number)
25040736964569129187…83631105273444270399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.504 Γ— 10⁹⁴(95-digit number)
25040736964569129187…83631105273444270401
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
5.008 Γ— 10⁹⁴(95-digit number)
50081473929138258374…67262210546888540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.008 Γ— 10⁹⁴(95-digit number)
50081473929138258374…67262210546888540801
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
1.001 Γ— 10⁹⁡(96-digit number)
10016294785827651674…34524421093777081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.001 Γ— 10⁹⁡(96-digit number)
10016294785827651674…34524421093777081601
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
2.003 Γ— 10⁹⁡(96-digit number)
20032589571655303349…69048842187554163199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.003 Γ— 10⁹⁡(96-digit number)
20032589571655303349…69048842187554163201
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
4.006 Γ— 10⁹⁡(96-digit number)
40065179143310606699…38097684375108326399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.006 Γ— 10⁹⁡(96-digit number)
40065179143310606699…38097684375108326401
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
8.013 Γ— 10⁹⁡(96-digit number)
80130358286621213399…76195368750216652799
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:57,775,613 XPMΒ·at block #6,816,435 Β· updates every 60s
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