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Block #453,592

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2014, 10:08:01 AM Β· Difficulty 10.3865 Β· 6,356,849 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d0a766c9878efd05be5ac77d68c337d275c9950a2bca9fd73c824a190262d3e
View on Chainz β†—

Height

#453,592

Difficulty

10.386472

Transactions

1

Size

199 B

Version

2

Bits

0a62efd0

Nonce

327,505

Timestamp

3/21/2014, 10:08:01 AM

Confirmations

6,356,849

Mined by

⛏️ P2SHARASAFQZafXLcFKMjXUc2bGWUSMNwky1f4

Merkle Root

8ebf09f461272a55f977d3c9327ab5f6fa8ab093735b98f62277cbf92ed4ce36
Transactions (1)
Coinbase8ebf09f461272a…77cbf92ed4ce36
1 in β†’ 1 out9.2600 XPM109 B
ARASAFQZ…MNwky1f4
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.

1.136 Γ— 10⁹⁴(95-digit number)
11364000772125609149…63456422870594504639
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
1.136 Γ— 10⁹⁴(95-digit number)
11364000772125609149…63456422870594504639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.136 Γ— 10⁹⁴(95-digit number)
11364000772125609149…63456422870594504641
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
2.272 Γ— 10⁹⁴(95-digit number)
22728001544251218298…26912845741189009279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.272 Γ— 10⁹⁴(95-digit number)
22728001544251218298…26912845741189009281
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
4.545 Γ— 10⁹⁴(95-digit number)
45456003088502436596…53825691482378018559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.545 Γ— 10⁹⁴(95-digit number)
45456003088502436596…53825691482378018561
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
9.091 Γ— 10⁹⁴(95-digit number)
90912006177004873193…07651382964756037119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.091 Γ— 10⁹⁴(95-digit number)
90912006177004873193…07651382964756037121
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
1.818 Γ— 10⁹⁡(96-digit number)
18182401235400974638…15302765929512074239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.818 Γ— 10⁹⁡(96-digit number)
18182401235400974638…15302765929512074241
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:57,727,612 XPMΒ·at block #6,810,440 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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