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Block #1,102,865

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2015, 4:22:21 PM Β· Difficulty 10.7522 Β· 5,701,179 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a81110ea9ec27efd6fecdbb4c6ed2afa88e3a2308d6947c8375a06a21919e2d9
View on Chainz β†—

Height

#1,102,865

Difficulty

10.752181

Transactions

2

Size

92.34 KB

Version

2

Bits

0ac08ef0

Nonce

1,045,213,275

Timestamp

6/13/2015, 4:22:21 PM

Confirmations

5,701,179

Mined by

⛏️ P2SHAJ9364Lk67MBANxHEDNRo61gtBgJyHR5PP

Merkle Root

5e5121247c436ed7b0e831bdad6920e419e6c6cdfaed63d8e0a1ff918db92270
Transactions (2)
Coinbase678c8c24ff66d8…c0cdf7a5aa58a4
1 in β†’ 1 out9.5900 XPM109 B
AJ9364Lk…gJyHR5PP
1e2070a06cd6c8…4c9187d264d08d
827 in β†’ 1 out7148.1750 XPM92.15 KB
ASD9H5dn…naPtLaLP
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.

7.325 Γ— 10⁹⁴(95-digit number)
73256618836957047261…57472619413358096639
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
7.325 Γ— 10⁹⁴(95-digit number)
73256618836957047261…57472619413358096639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.325 Γ— 10⁹⁴(95-digit number)
73256618836957047261…57472619413358096641
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
1.465 Γ— 10⁹⁡(96-digit number)
14651323767391409452…14945238826716193279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.465 Γ— 10⁹⁡(96-digit number)
14651323767391409452…14945238826716193281
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
2.930 Γ— 10⁹⁡(96-digit number)
29302647534782818904…29890477653432386559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.930 Γ— 10⁹⁡(96-digit number)
29302647534782818904…29890477653432386561
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
5.860 Γ— 10⁹⁡(96-digit number)
58605295069565637809…59780955306864773119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.860 Γ— 10⁹⁡(96-digit number)
58605295069565637809…59780955306864773121
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
1.172 Γ— 10⁹⁢(97-digit number)
11721059013913127561…19561910613729546239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.172 Γ— 10⁹⁢(97-digit number)
11721059013913127561…19561910613729546241
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:57,676,405 XPMΒ·at block #6,804,043 Β· updates every 60s
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