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Block #513,601

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/27/2014, 3:26:24 PM Β· Difficulty 10.8356 Β· 6,296,854 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d3331f6d0022ad159d4afadebc975a98974f2c2a92019d4433021cba14509fa
View on Chainz β†—

Height

#513,601

Difficulty

10.835649

Transactions

1

Size

187 B

Version

2

Bits

0ad5ed1c

Nonce

60,683

Timestamp

4/27/2014, 3:26:24 PM

Confirmations

6,296,854

Mined by

⛏️ AaSAYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

d8a0433118b83b7383c9465220389a6820690f2407deae3120fb04937143ea55
Transactions (1)
Coinbased8a0433118b83b…fb04937143ea55
1 in β†’ 1 out8.5000 XPM97 B
AYCeLhqB…eqGM6KK1
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.

3.002 Γ— 10⁹⁴(95-digit number)
30024336861380759920…31938385157957232519
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
3.002 Γ— 10⁹⁴(95-digit number)
30024336861380759920…31938385157957232519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.002 Γ— 10⁹⁴(95-digit number)
30024336861380759920…31938385157957232521
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
6.004 Γ— 10⁹⁴(95-digit number)
60048673722761519840…63876770315914465039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.004 Γ— 10⁹⁴(95-digit number)
60048673722761519840…63876770315914465041
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
1.200 Γ— 10⁹⁡(96-digit number)
12009734744552303968…27753540631828930079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.200 Γ— 10⁹⁡(96-digit number)
12009734744552303968…27753540631828930081
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
2.401 Γ— 10⁹⁡(96-digit number)
24019469489104607936…55507081263657860159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.401 Γ— 10⁹⁡(96-digit number)
24019469489104607936…55507081263657860161
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
4.803 Γ— 10⁹⁡(96-digit number)
48038938978209215872…11014162527315720319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.803 Γ— 10⁹⁡(96-digit number)
48038938978209215872…11014162527315720321
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:57,727,726 XPMΒ·at block #6,810,454 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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