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Block #294,539

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2013, 10:28:11 PM Β· Difficulty 9.9911 Β· 6,514,792 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c49d3dc11842abff14d7be0b42ee385a59e6992a0080fabc799c1c53ea6e114b
View on Chainz β†—

Height

#294,539

Difficulty

9.991072

Transactions

2

Size

357 B

Version

2

Bits

09fdb6e0

Nonce

18,638

Timestamp

12/4/2013, 10:28:11 PM

Confirmations

6,514,792

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bc4ea1df7d5bccd9a3566d3418b5929605122aedea1ce7570982dd7f8107bb18
Transactions (2)
Coinbase374c3cc1d2f82a…bb5a811e7c00ec
1 in β†’ 1 out10.0100 XPM110 B
AeKNrjNj…1NEq95Ta
b748651c4e7584…39b59dcbab71cf
1 in β†’ 1 out10.1600 XPM157 B
AMWKfUWU…hjT6U8ko
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.

6.939 Γ— 10⁹⁡(96-digit number)
69398748644763187775…53175704149529162399
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
6.939 Γ— 10⁹⁡(96-digit number)
69398748644763187775…53175704149529162399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.939 Γ— 10⁹⁡(96-digit number)
69398748644763187775…53175704149529162401
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
1.387 Γ— 10⁹⁢(97-digit number)
13879749728952637555…06351408299058324799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.387 Γ— 10⁹⁢(97-digit number)
13879749728952637555…06351408299058324801
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
2.775 Γ— 10⁹⁢(97-digit number)
27759499457905275110…12702816598116649599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.775 Γ— 10⁹⁢(97-digit number)
27759499457905275110…12702816598116649601
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
5.551 Γ— 10⁹⁢(97-digit number)
55518998915810550220…25405633196233299199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.551 Γ— 10⁹⁢(97-digit number)
55518998915810550220…25405633196233299201
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
1.110 Γ— 10⁹⁷(98-digit number)
11103799783162110044…50811266392466598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.110 Γ— 10⁹⁷(98-digit number)
11103799783162110044…50811266392466598401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,718,714 XPMΒ·at block #6,809,330 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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