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Block #463,581

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/28/2014, 5:50:18 AM Β· Difficulty 10.4128 Β· 6,349,445 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
40bfd19f51b4d309219e9292f03822aabb37a79b1642bbe5cca394e36f94c58d
View on Chainz β†—

Height

#463,581

Difficulty

10.412843

Transactions

2

Size

15.43 KB

Version

2

Bits

0a69b011

Nonce

53,591

Timestamp

3/28/2014, 5:50:18 AM

Confirmations

6,349,445

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b7939059c7f56da03338c9be8757fe862ff2fe36f46e01e0f62ab84965d42557
Transactions (2)
Coinbase4eea2bf4881f53…4ebf18f22684ed
1 in β†’ 1 out9.3700 XPM110 B
AeKNrjNj…1NEq95Ta
049465abf4f946…72b79f210045c6
105 in β†’ 2 out321.0126 XPM15.24 KB
ASdPorb4…PVPHUQ5YAT6XraPv…6QRxJMf9
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.

1.563 Γ— 10⁹⁡(96-digit number)
15633894000763642013…94580547065249634559
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
1.563 Γ— 10⁹⁡(96-digit number)
15633894000763642013…94580547065249634559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.563 Γ— 10⁹⁡(96-digit number)
15633894000763642013…94580547065249634561
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
3.126 Γ— 10⁹⁡(96-digit number)
31267788001527284026…89161094130499269119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.126 Γ— 10⁹⁡(96-digit number)
31267788001527284026…89161094130499269121
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
6.253 Γ— 10⁹⁡(96-digit number)
62535576003054568052…78322188260998538239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.253 Γ— 10⁹⁡(96-digit number)
62535576003054568052…78322188260998538241
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
1.250 Γ— 10⁹⁢(97-digit number)
12507115200610913610…56644376521997076479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.250 Γ— 10⁹⁢(97-digit number)
12507115200610913610…56644376521997076481
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
2.501 Γ— 10⁹⁢(97-digit number)
25014230401221827220…13288753043994152959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.501 Γ— 10⁹⁢(97-digit number)
25014230401221827220…13288753043994152961
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:57,748,250 XPMΒ·at block #6,813,025 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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