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Block #1,145,814

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/9/2015, 1:10:51 AM Β· Difficulty 10.9318 Β· 5,667,215 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf55de912b98db4364517b89ea28f7587d5ad461f7738ee31115faa975b4fcec
View on Chainz β†—

Height

#1,145,814

Difficulty

10.931833

Transactions

2

Size

7.06 KB

Version

2

Bits

0aee8c9e

Nonce

23,058,947

Timestamp

7/9/2015, 1:10:51 AM

Confirmations

5,667,215

Mined by

⛏️ P2SHAWacJRv2Nv5y1MYBYd8Bu17U1EuLNuAaXq

Merkle Root

826c1e5fcb13c04fa9b2a5ed298217efef9eb0689c2085e436c32e600f47531e
Transactions (2)
Coinbase140618a40bdb91…774452248b9c71
1 in β†’ 1 out8.4300 XPM110 B
AWacJRv2…uLNuAaXq
5cea6fcceae5c6…2b73927dffc98a
47 in β†’ 2 out500.0100 XPM6.87 KB
ARedwex8…c5RU3X8QAJjnK9uC…VreFquR4
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.

1.246 Γ— 10⁹³(94-digit number)
12462743375548898645…69830738241812648719
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
1.246 Γ— 10⁹³(94-digit number)
12462743375548898645…69830738241812648719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.246 Γ— 10⁹³(94-digit number)
12462743375548898645…69830738241812648721
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
2.492 Γ— 10⁹³(94-digit number)
24925486751097797291…39661476483625297439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.492 Γ— 10⁹³(94-digit number)
24925486751097797291…39661476483625297441
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
4.985 Γ— 10⁹³(94-digit number)
49850973502195594582…79322952967250594879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.985 Γ— 10⁹³(94-digit number)
49850973502195594582…79322952967250594881
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
9.970 Γ— 10⁹³(94-digit number)
99701947004391189164…58645905934501189759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.970 Γ— 10⁹³(94-digit number)
99701947004391189164…58645905934501189761
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
1.994 Γ— 10⁹⁴(95-digit number)
19940389400878237832…17291811869002379519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.994 Γ— 10⁹⁴(95-digit number)
19940389400878237832…17291811869002379521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.988 Γ— 10⁹⁴(95-digit number)
39880778801756475665…34583623738004759039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,748,274 XPMΒ·at block #6,813,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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